Ecole Sigle

Doctorale

Renée El

Melhem Bât

Pascal Blaise

R Gourdon

M Stéphane

ÉLECTROTECHNIQUE E E A Électronique

M Gérard Scorletti
email: gerard.scorletti@ec-lyon.fr

M Philippe
email: philippe.normand@univ-lyon1.fr

Mme Emmanuelle
email: emmanuelle.canet@univ-lyon1.fr

M Luca

Jean-Yves Buffière
email: jean-yves.buffiere@insa-lyon.fr

Stéphanie Cauvin

M Jocelyn Bonjour

Véronique Guichard

J Y Toussaint

M Christian Montes

Nathan Blanken

Collaborative Filtering CTR Click-Through Rate DNN Deep Neural Network DPP Determinantal Point Process KE

Keywords: Recommender Systems, Diversity, Accuracy, Knowledge Graph Embedding, Determinantal Point Processes. i diversity results before diversification method for anime datasets

Recommender systems (RS) have been widely applied in real life scenarios to constantly provide personalised recommendation to satisfy users' need. In classical top-N recommendation models, historical user-item interactions are collected and exploited to learn and predict for each user a top-N item list. But we are also aware that both user-side and item-side auxiliary information may help to improve the recommendation performance. At the same time, in terms of recommendation performance, accuracy has been the main research focus in recommender systems, though works have pointed out that an optimal accuracy is not equal to an optimal satisfaction of users towards recommendation. An accuracy-centric recommendation model may create an isolate, singular and redundant atmosphere when providing the service, thus it is essential to bring other goals in RS to alleviate these problems.

In this dissertation, we focus on bringing diversity along with accuracy as recommendation goals, as we argue that a diversified recommendation helps alleviate the problems suffered by accuracy-centric RS. We also take item-side auxiliary information into account for enhancing accuracy. Thus we propose diversity-aware top-N recommendations based on knowledge graph embedding to aim at achieving both high accuracy and high diversity in recommendation lists for users.

Our first contribution is DivKG, a diversified recommendation framework that combines knowledge graph embedding and determinantal point processes (DPP). We propose a new personalised DPP kernel matrix construction method that uses knowledge graph embedding results for DPP diversification.

Our second contribution is EMDKG, a diversified recommendation framework which encodes semantic diversity into item representations and achieve better trade-off compared to state-of-the art methods in terms of accuracy and diversity.

Résumé

Les systèmes de recommandation (RS) sont largement appliqués dans la vie réelle pour fournir des recommandations personnalisées pour satisfaire les besoins des utilisateurs. Dans les modèles de recommandation top-N classiques, les historiques d'interactions entre utilisateur et éléments sont recueillies et exploitées pour apprendre et prédire des listes de top-N éléments. Mais nous sommes également conscients que les informations auxiliaires côté utilisateur et côté élément peuvent contribuer à améliorer la qualité des recommandations. En termes de mesures de performance de recommandation, la précision a été le principal objectif dans le domaine, bien que des travaux aient souligné qu'une précision optimale n'égale pas une satisfaction optimale des utilisateurs vis-à-vis de la recommandation. Un modèle de recommandation centré sur la précision peut renvoyer des résultats redondants lors de la fourniture du service. Il est donc essentiel d'apporter d'autres objectifs dans la recommandation pour atténuer ces problèmes.

Dans cette thèse, nous nous concentrons sur l'étude conjointe de la diversité et de la précision en tant qu'objectifs de recommandation, car nous considérons qu'une recommandation diversifiée aide à atténuer les problèmes générés par la recommandation centrée sur la précision. Nous prenons également en compte les informations auxiliaires côté élément pour améliorer la précision. Ainsi, nous proposons des recommandations diversifiées top-N basées sur le plongement de graphes de connaissances pour atteindre à la fois une haute précision et une grande diversité dans les listes de recommandations.

Notre première contribution est DivKG, un modèle qui combine le plongement de graphes de connaissances (KGE) et les processus ponctuels déterminantaux (DPP). Nous proposons une nouvelle méthode de construction de matrice de noyau DPP personnalisée qui utilise des résultats de KGE pour la diversification DPP.

Notre deuxième contribution est EMDKG, un modèle qui encode la diversité sémantique dans les représentations d'éléments et réalise un meilleur compromis par rapport aux méthodes de l'état de l'art en termes de précision et de diversité.

Mots-clés: Systèmes de recommandation; Diversité; Précision; Plongement des Graphes de Connaissance; Processus Ponctuels Déterminants.

ii Declaration by the candidate I hereby declare that this thesis is my own work and effort and that it has not been submitted anywhere for any award. Where other sources of information have been used, they have been marked. The work has not been presented in the same or a similar form to any other testing authority and has not been made public.

I hereby also entitle a right of use (free of charge, not limited locally and for an indefinite period of time) that my thesis can be duplicated, saved and archived by INSA-Lyon, LIRIS laboratory and Infomaths doctoral school.

Lyon, May 18, 2022 iii List of Figures 6.1 A content-based filtering method create user profiles from historical preferred items' content and a recommendation can be generated by finding similar items to user profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 A collaborative filtering method learns from historical user-item interaction to find similar users(explicitly or implicitly). For generating personalized results, items that are preferred by similar users will constitute into a recommendation list for user. . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 A binarized rating matrix where each column represents the rating scores an item receives and each row represents the rating scores a user gives. The rating score 1 means a positive preference or like between a pair of user and item; and 0 means a negative preference or dislike between a pair of user and item. A '?' for rating score means no historical rating of this pair of user and item. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 On the left, there is a knowledge graph for part of MovieLens data, including entities (movies, staff working for the movies, genres) and relations connecting the entities (InActorOf, IsInGenre etc.). On the right it is the latent embedding space where both entities and relations are embedded into. Knowledge graph embedding methods map elements of a knowledge graph (including both entities and relations) into the latent space while conserving the graph structure(node similarity etc.). . . . . . . . . . . . . . 7.2 Simple illustrations of TransE and TransH. Source: [START_REF] Wang | Knowledge graph embedding by translating on hyperplanes[END_REF]. . . . . . . . . . . . 7.3 A simple illustration of TransD. Source: [START_REF] Ji | Knowledge graph embedding via dynamic mapping matrix[END_REF]. . . . . . . . . . . . . . . . . .

An example of long-tail effect distribution chart. The horizontal axis

represents the number of items in this distribution; and the vertical axis represents the occurrences of searches for items. The pink area on the left is the dominant "head" of the distribution while the green area shows a long tail of huge number of items with low searches. . . . . . . . . . . . . . . . 11.1 DivKG: a diversity enhancing recommendation framework based on knowledge graph embedding methods. Datasets are preprocessed to extract entityrelation triplets for constructing knowledge graphs for recommendation.

Then given such a knowledge graph, we learn the vectorial representations of entities and relations by applying different knowledge graph embedding methods. After obtaining the latent vectors of users, items, other entities and relations, personalized kernel matrix can be constructed for each user. Finally we render each user a diversified recommendation list of items by the fast greedy MAP inference algorithm on its corresponding kernel matrix. 11. [START_REF] Chen | A music recommendation system based on music data grouping and user interests[END_REF] The anime genres are comedy, action, fantasy, sci-fi, drama, shounen, kids, romance, school, slice of life, hentai, supernatural, mecha, music, historical, magic, ecchi, shoujo, seinen, sports, mystery, super power, military, parody, space, horror, harem, demons, martial arts, dementia, psychological, police, game, samurai, vampire, thriller, cars, shounen ai, shoujo ai, josei, yuri, yaoi, and other. . M candidate items, we construct a M × M dimension matrix where the diagonal element representing the affinities of each item towards the user (a u1 for example represents the affinity or relevance for item 1 towards user u) ;and non-diagonal element representing the pairwise similarity of items (d 3M for example represents the similarity between item 3 and item M ). Due to the properties of DPP, such a kernel matrix will garantee a set of items with high affinity and diversity will be more likely to be selected from all candidate items. . Recommender systems have been prevalent for three decades in various domains, ranging from web personalisation [START_REF] Mobasher | Automatic personalization based on web usage mining[END_REF], music [START_REF] Chen | A music recommendation system based on music data grouping and user interests[END_REF][START_REF] Kuo | Emotion-based music recommendation by association discovery from film music[END_REF], news [START_REF] Bomhardt | Newsrec, a svm-driven personal recommendation system for news websites[END_REF], book recommendation [START_REF] Paula | Improving a hybrid literary book recommendation system through author ranking[END_REF] to e-commerce [START_REF] Sundaresan | Recommender systems at the long tail[END_REF], group recommendation [START_REF] Da Cao | Attentive group recommendation[END_REF] and other domain-specific application. Recommender systems arise from the phenomenon of information overload on the internet, which makes it difficult for online consumers to receive relevant information. Thus, the existing systems have already proven the huge potential benefits of providing personalized information to their users. Indeed, immersing in such ample quantity of information of different kinds, whether on a news webpage or a social media platform for example, users are easily overwhelmed by the quantity of data or information and it is infeasible to go through all the information for them alone. Thus, it is necessary and of great interest for both users and information providers to apply personalization or recommender systems to filter unrelated information for the users.

List of Tables

In different contexts of applications, the information to be personalized is called differently and item as a term is widely used to refer to a unit of information to be recommended or personalized. Thus, a recommender system is essentially composed of two roles: users who are to receive recommendation items and items which are to be selected and recommended to the users. The method and process of recommendation or personalized selection is the bridge connecting these two by generating the recommendation through recommendation algorithms.

Unlike other information retrieval problems [START_REF] Van Rijsbergen | Information retrieval: New directions: Old solutions[END_REF][START_REF] Berger | Information retrieval as statistical translation[END_REF] where queries are given to indicate what users are looking for, no direct and explicit requests (in forms of queries for example) are given in a scenario of recommendation. However, by analyzing and processing historical interactions between users and items and other available information relating users and items, we can detect to a certain degree the preference and taste of users towards items. Thus, recommendation algorithms aim to exploit the historical interactions and other available information to the maximum for generating good personalized recommendations for each user.

By intuition, a good recommendation is one that recommends suitable items to users according to each user's personal taste. However, users' personal tastes are not explicitly given by users themselves and should be inferred in recommendation algorithms given various types of available data. Traditionally, by utilizing various types of data through different approaches, three main paradigms of recommender systems have emerged in recommendation algorithm researches, namely collaborative filtering [START_REF] Resnick | Grouplens: An open architecture for collaborative filtering of netnews[END_REF] methods, contentbased filtering [START_REF] Cano | Content-based music audio recommendation[END_REF] methods and hybrid filtering methods [START_REF] Balabanović | Fab: Content-based, collaborative recommendation[END_REF][START_REF] Mateus | /i> and the adaptive recommendation project[END_REF] combining the previous two.

Collaborative filtering (CF) methods derive from an assumption that a user may find an item interesting if this item is liked by another user who shares the tastes of the user in question. Departing from this assumption, CF methods aim at finding similar users for each user in order to recommend items preferred by similar users. It is obvious that CF methods can exploit user-item historical interaction data for the recommendation.

The second paradigm is Content-based filtering (CBF) methods which build the recommendations on another assumption. They consider the process from the item side instead of user side and assume that an item may interest a user if this item is similar to the items that are already liked by this user. That it to say, CBF methods compare items to each user's historical preferable items and recommend items most similar to the historical items as results. In order to find similar items for each item, item-side information will be used for measuring the similarities.

And the third paradigm hybrid filtering methods combine the collaborative and contentbased filtering to leverage both user similarities and item similarities for better performance. To achieve this, both historical user-item interactions and item-side information are required. And different hybrid filtering methods exploit the available data to build more complex structures to benefit to the best.

Although huge quantities of innovative works in these three paradigms have been explored by researchers in the domain, the optimization of finding a better recommendation does not stop due to lack of theoretical upper bound for the problem and variety of available data in specific contexts. Particularly, given various types of data relating users and items which can potentially leverage a better recommendation result, there is still lack of a general and simple solution to fully exploit the knowledge hidden inside the data. Knowledge graph embedding methods [START_REF] Bordes | Translating embeddings for modeling multi-relational data[END_REF][START_REF] Wang | Knowledge graph embedding by translating on hyperplanes[END_REF][START_REF] Yang | Embedding entities and relations for learning and inference in knowledge bases[END_REF][START_REF] Mehran | Simple embedding for link prediction in knowledge graphs[END_REF] have recently attracted huge attention in research for many machine learning tasks, such as node classification, link prediction and graph completion. A few proposals [START_REF] Zhang | Collaborative knowledge base embedding for recommender systems[END_REF][START_REF] Xin | Relational collaborative filtering: Modeling multiple item relations for recommendation[END_REF] using knowledge graph embedding combined with collaborative filtering for recommendation have also achieved better results than traditional approaches. In terms of knowledge graphs, users and items can be seen as entities, whereas preference of a user regarding an item can be seen as a kind of relation, link between corresponding entities. From this perspective, a recommendation task can be formulated as an instance of the link prediction problem. Besides, along with user-item preference information, item-side auxiliary information can also be represented in form of (entity, relation, entity). Thus we consider it rather reasonable to build a model based on knowledge graph embedding to find a simple yet efficient solution to recommend taking into account multi-type information source.

When we go beyond intuition and reason what a good recommendation is, accuracy has been the first and in most cases the only criterion. Take a CF-based recommender system in industrial scenarios as an example. Such a system implemented on a certain platform consumes huge amount of interaction data between users and items available on the platform to predict users' potential need. The prediction or recommendation to users are expected to be accurate, as non-related item recommendation may disappoint user and thus discourage user from engaging to the platform.

However, recent works [START_REF] Ziegler | Improving recommendation lists through topic diversification[END_REF] have pointed out the inability of focusing solely on accuracy to satisfy users' interest. One example is that recommending two over-similar items to one user may produce redundancy in the result. Similar to an information retrieval scenario, a user expects a recommendation of items to satisfy her interests while still not being duplicates.

Another example is if the user only had a limited range of item interaction history, the recommendation based on such information will also generate highly similar items thus creating "filter bubbles" [START_REF] Pariser | The Filter Bubble: What the Internet Is Hiding from You[END_REF] for the users. The term "filter bubble" is brought by Eli Pariser, and designates the isolation effect resulting from the use of algorithms aiming to selectively guess what a user would like based on clicking and search history, separating users from different and opposing viewpoints. The viewpoint narrowing can result in users staying in their cultural or ideological bubbles, exposing them to fake news and the phenomenon of echo chambers, which potentially endangers the RS ecosystem or even the whole internet atmosphere.

Thus, in addition to accuracy, diversity of recommendation has been brought up as part of recommendation performance. Furthermore, various user studies [START_REF] Nguyen | Exploring the filter bubble: The effect of using recommender systems on content diversity[END_REF][START_REF] Ferwerda | How item discovery enabled by diversity leads to increased recommendation list attractiveness[END_REF][START_REF] Wu | Does diversity affect user satisfaction in image search[END_REF] have confirmed that an exposure to diverse items in recommendation has a positive effect over item list attractiveness towards higher user satisfaction.

As recommendation accuracy is not equivalent to user satisfaction with recommender systems, diversity is introduced as another recommendation goal besides accuracy. Though it is intuitive that a diverse recommendation should provide a list of items one dissimilar to the other as much as possible without compromising its recommendation accuracy, more investigation into how to define and evaluate dissimilarity of items should be given. Diversity of recommendation results can be understood on two levels, the individual level which corresponds to individual recommendation list diversity and the group (or aggregate) level which corresponds to the general item distribution over all users.

Aggregate diversity [START_REF] Vargas | Improving sales diversity by recommending users to items[END_REF][START_REF] Eskandanian | Using Stable Matching to Optimize the Balance between Accuracy and Diversity in Recommendation[END_REF][START_REF] Eskandanian | Using Stable Matching to Optimize the Balance between Accuracy and Diversity in Recommendation[END_REF] targets at improving a more feature-balanced recommendation over all items towards user and alleviating the long-tail effect [START_REF] Sundaresan | Recommender systems at the long tail[END_REF][START_REF] Hongzhi Yin | Challenging the long tail recommendation[END_REF] as much as possible. The long-tail effect is that there is a high frequency of very few well-recognized items exposed to users while large proportion of obscure items have extremely low chance to get exposed.

In contrast, individual diversity aims at providing a diversified personalized item list to each user to enhance personal experience and satisfactions of users with recommender systems. Improving the individual level diversity is a direct solution to redundancy and filter bubble issues. There exist different diversification methods aiming at improving individual diversity [START_REF] Carbonell | The use of mmr, diversity-based reranking for reordering documents and producing summaries[END_REF][START_REF] Borodin | Max-sum diversification, monotone submodular functions, and dynamic updates[END_REF] in information retrieval. These diversification approaches rely on pairwise dissimilarities among items, however the concept of dissimilarity is coupled with diversity, varying in specific scenarios. Thus, when applying a diversification model to a new accuracy-centered recommendation the effectiveness of such diversification still needs to be verified. More recently diversity models [START_REF] Kulesza | k-dpps: Fixed-size determinantal point processes[END_REF][START_REF] Kulesza | Learning determinantal point processes[END_REF] such as the ones based on determinantal point processes which capture the both diversity features and user-item relevance within models themselves have caught huge attention. Therefore, it is of great interest to investigate whether such diversity models can be employed for diversified recommendation.

Problem Statement

Given the context of recommender systems, our research conducted in this dissertation target at answering the following research questions.

RQ 1: How can we incorporate knowledge graph embedding for a recommendation to take into account multiple types of information?

As we are interested in incorporating knowledge graph embedding methods into a top-N recommendation for processing both historical user-item interactions and item-side information, it is then the most fundamental question to decide how we can do this for both learning the representations and making top-N predictions based on learned models.

RQ 2: How can we combine knowledge graph embedding results with diversification methods? In particular, how can we incorporate knowledge graph embedding with determinantal point processes for a top-N recommendation?

The second question corresponds to our determination to propose a diversified recommendation. Following RQ 1, as we decide to incorporate knowledge graph embedding for recommendation, we then need to conceive efficient diversification methods that make use of knowledge graph embedding results. As we are interested in the diversification model -determinantal point processes which can capture both user-item relevance and item diversity, it is then fundamental to propose an approach to effectively link the two models.

RQ 3: How can we evaluate the performance of a diversified recommendation?

The third research question is to answer how we can quantify the performance of diversified recommendation. As a diversified recommendation has two goals accuracy and diversity to achieve, it is not simply about to optimize the two separate goals. The correlations of these two goals must be taken into consideration for achieving a both accurate and diverse recommendation. On the other hand, the concept of individual diversity still varies according to a specific context, it is then essential to discuss whether a diversified recommendation can accommodate various definitions of individual diversities.

To resume, in this dissertation we target at improving individual diversity on a top-N recommendation problem. A top-N recommendation is to recommend each user a list of the length of N items from all the candidate items by learning from historical user-item interactions and other accessible auxiliary information. In addition to provide accurate recommendation results to the users, we consider another quality -the diversity measurement of each recommendation list as our optimization goal. In the end, for each user, we aim to provide a both accurate and diverse item list consisting of N items.

Contributions

The contributions of this thesis are two-fold: (1) DivKG: Improving Recommendation Diversity Based on Knowledge Graph; (2) EMDKG: Diversity-Aware Representation Learning for a Better Trade-off Diversified Recommendation. More precisely these two contributions answer our research question described below.

RQ1: How can we incorporate knowledge graph embedding for a recommendation with multiple types of information?

To answer this research question, we have established an approach for both DivKG and EMDKG to construct a recommendation knowledge graph which contains both user-item interactions and item-side auxiliary information. We note that user-item interactions can be regarded as a special type of relational triplets, where each instance resembles to (user, pref erence, item) and pref erence is the special relation between user and item.

For item-side auxiliary information, relational triplets can also be extracted by identifying a relational instance composed of an item, a relation type and a related entity, denoted as (item, relation, entity).

RQ2: How can we combine knowledge graph embedding results

with diversification methods? In particular, how can we incorporate knowledge graph embedding with determinantal point processes for a top-N recommendation?

To address this research question, we first clarify that the combination of knowledge graph embedding with diversification methods can occur during the model learning phase and the diversified recommendation generation phase. In DivKG, our core contribution regarding this RQ is that we propose a novel approach of constructing personalized determinantal point process kernel matrix based on knowledge graph embedding during the recommendation generation phase. And in EMDKG, the diversification model incorporates both knowledge graph embedding learning phase and the diversified recommendation generation phase. This modification comparing to DivKG actually guarantees to encode explicitly a selected individual diversity into the item latent vectors, which can improve the diversity performance for final recommendation results.

RQ3: How can we evaluate the performance of a diversified recommendation?

After the proposal of diversified recommendation models, we need to support the models with experimental results based on real life datasets (MovieLens-IMDb datasets and Anime datasets) for assessing the effectiveness of the approaches. As the performance of a diversified recommendation considers both accuracy and diversity aspects, we use both accuracy metrics and diversity metrics for measuring the performance of DivKG and EMDKG. For the accuracy we employ two accuracy metrics Hit and NDCG on both DivKG and EMDKG. And for diversity metrics, we employ vector list dissimilarity ILMD and ILAD for DvKG and categorical information based metrics Category Coverage (CC) and α-NDCG in EMDKG.

Publications and Communications

These contributions were submitted and accepted by the following international/national conferences:

International publications

Scientific Communications

During this thesis, the following communications/presentations have been made on the topic of diversified recommendation:

Plan of the Dissertation

This dissertation is organized as follows. In Part II, we introduce the state-of-the-art researches related to my research topics. First, we present recommender systems (Chapter 6) providing a general overview of the domain, then we describe knowledge graph embedding (KGE) techniques and KGE-based recommendation (Chapter 7), and finally, we discuss diversity-aware information retrieval and recommendation (Chapter 8). In Part III, we introduce the proposed models corresponding to our two contributions, DivKG and EMDKG. In Part IV, we provide the evaluation of our two contributions. Finally, in Part V, we present our conclusions and future directions. Recommender systems have been prevalent for three decades, arising from overloading information and the need for filtering overwhelming quantity of information, on the one hand, and the interest of personalized information towards information consumers. Over the decades, various techniques and structures have been proposed to satisfy this personalization given a plethora of information related to both information consumers and recommended content itself. A recommender system is essentially composed of two type of components: items which are to be selected for constucting the personalized recommendation list and users who receive a list of items. Various types of information can be used for this personalization process, including user-item information, user-side auxiliary information and item-side information.

Part II

State of the Art

In this chapter we introduce the traditional three categories of recommender systems, namely content-based filtering, collaborative filtering and hybrid methods.

Content-Based Filtering Recommender Systems

Content-based filtering (CBF) methods [START_REF] Foltz | Personalized information delivery: An analysis of information filtering methods[END_REF][START_REF] Lops | Content-based recommender systems: State of the art and trends[END_REF] are the first approaches of personalized information filtering to overcome information overload problems. As indicated by its name, the idea of content-based filtering is to build user profiles based on user preferred content and by matching new items' content with the user profile we can create recommendation lists. In Figure .6.1 we demonstrate the idea of content-based filtering for recommendation.

In order to build user profiles based on user preferred content, two tasks are required. The first task is to analyze historically preferred items' content (traditionally in textual data, denoted as Content(i) for item i) to extract features or properties for representing the items. The second task is to collect and aggregate the features and properties of all items that are liked by a user to build and learn a corresponding user profile for item recommendation. Naturally both representing items and user profiles can employ different methods.

For the first task, as the items' content is usually textual data, vector space model (VSM) and extended language models, e.g.term frequency-inverse document frequency (TF-IDF) [START_REF] Luhn | A statistical approach to mechanized encoding and searching of literary information[END_REF][START_REF] Spärck | A statistical interpretation of term specificity and its application in retrieval[END_REF], pLSA [START_REF] Hofmann | Probabilistic latent semantic analysis[END_REF] and LDA [START_REF] Blei | Latent dirichlet allocation[END_REF], have been applied for item representation in CBF. For content-based methods which have employed TF-IDF, items are represented as weighted term vectors. More specifically, as items are originally represented as textual data or documents, the set of |I| items is denoted as I = i 1 , ..., i |I| and the content of the items is represented as the set Content(I) = Content(i 1 ), Content(i 2 ), ..., Content(i |I| ) , and T erms = {t 1 , t 2 , ..., t m } is the set of terms appeared in all the documents/items or called as dictionary.

For each item i, the content is a collection of l terms, denoted as

Content(i) = {t i,
i)) = f k,i max j f j,i log n n k (6.2)
where f k,i is the frequency of term t i,k in item content Content(i) and n k is the number of documents in which the term t i,k has appeared at least once. Thus, an item content Content(i) can be the represented as a vector of similarities with all terms, denoted as Content(i) = {w i,1 , w i,2 , ..., w i,l }, where w i,k , k ∈ {1, 2, .., l} is given in Eq.(6.1).

For the second task to analyze and to learn user profiles, several ways have been proposed. The first and also intuitive way is to represent the user profile in a similar way as item content. In a similar fashion, the user profile for user u is composed of terms T erms, denoted as ContentBasedP rof ile(u) = {w u,1 , w u 2 , ..., w u,l }. Then for recommendation the relevance between user u and item i can be calculated based on a score function based on the weighted term vectors in item content and user profile, written as, relevance(u, i) = score(ContentBasedP rof ile(u), Content(i)) (6.3) Another way [START_REF] Lang | Newsweeder: Learning to filter netnews[END_REF][START_REF] Mooney | Content-based book recommending using learning for text categorization[END_REF] for learning user profiles is to regard the recommendation task as a binary text categorization task: given a new item with its content, the acquired user profile can match this item and predict whether it belongs to the positive or negative category, where positive means this item will compose the recommendation list and negative means the opposite. Even though by recommending items with similar content can to a certain extend satisfy users' need because of the correlation between the content of items and users' preference, content-based filtering has been pointed out suffering from the following limitations [START_REF] Lops | Content-based Recommender Systems: State of the Art and Trends[END_REF]:

-Content-based filtering approaches in general supply a very shallow analysis of content [START_REF] Balabanović | Fab: Content-based, collaborative recommendation[END_REF] and can not provide items based on the assessment of quality or opinions. A highly rated item is no different to a poorly rated item if the content of them are highly similar or identical.

-Content-based approaches tend to produce overspecialization [START_REF] Adomavicius | Toward the next generation of recommender systems: a survey of the state-of-the-art and possible extensions[END_REF] in recommendation due to only comparing item content to historical items' content which may represent users' taste with bias.

-Coupling to the second point, content-based filtering approaches do not have a way to find serendipitous items for users. A serendipitous item to a user is one could satisfy the user's taste but is poorly relevant to user's historical interactions.

Due to these limitations, other filtering techniques have been proposed, and one type is particularly successful and has been widely used, which is collaborative filtering.

Collaborative Filtering Based Recommender Systems

.2: A collaborative filtering method learns from historical user-item interaction to find similar users(explicitly or implicitly). For generating personalized results, items that are preferred by similar users will constitute into a recommendation list for user.

Collaborative filtering (CF) is a category of techniques which are frequently used in recommendation and personalization and often achieve good performance in terms of accuracy. The main idea of CF is that a user's taste can be inferred through collecting and analyzing the tastes of similar users. To determine similar users of one particular user, the historical interactions between users and items can be used. There are various approaches to collect and use historical user-item interactions for inferring user's taste, and regarding the way of using the information, CF methods are in general categorized into Memory-Based collaborative filtering [START_REF] Resnick | Grouplens: An open architecture for collaborative filtering of netnews[END_REF][START_REF] Shardanand | Social information filtering: Algorithms for automating "word of mouth[END_REF][START_REF] Sarwar | Item-based collaborative filtering recommendation algorithms[END_REF] and Model-Based collaborative filtering [START_REF] Billsus | Learning collaborative information filters[END_REF][START_REF] Goldberg | Eigentaste: A constant time collaborative filtering algorithm[END_REF][START_REF] Salakhutdinov | Probabilistic matrix factorization[END_REF][START_REF] Rendle | Bpr: Bayesian personalized ranking from implicit feedback[END_REF][START_REF] Kabbur | Fism: Factored item similarity models for top-n recommender systems[END_REF][START_REF] Wang | Irgan: A minimax game for unifying generative and discriminative information retrieval models[END_REF]. In Figure .6.2, we show the idea of collaborative filtering for recommending items to users.

Memory-Based Collaborative Filtering

As CF methods determine users' tastes by analyzing from historical user-item interactions, memory-based collaborative filtering [START_REF] Resnick | Grouplens: An open architecture for collaborative filtering of netnews[END_REF][START_REF] Shardanand | Social information filtering: Algorithms for automating "word of mouth[END_REF][START_REF] Sarwar | Item-based collaborative filtering recommendation algorithms[END_REF][START_REF] Breese | Empirical analysis of predictive algorithms for collaborative filtering[END_REF][START_REF] Yu | Instance selection techniques for memory-based collaborative filtering[END_REF][START_REF] Deshpande | Item-based top-<i>n</i> recommendation algorithms[END_REF] directly use the historical rating data to calculate the relevance or similarity between users and items. This category of CF methods get their name by only needing to memorize the historical user-item interactions such as the rating data. We denote the historical rating data as Rating(U ) = Rating(u 1 ), Rating(u 2 ), ..., Rating(u |U | ) , where Rating(u) = {rating u,i |i ∈ I u } represents the collection of ratings the user u has given towards different items I u . Thus, to predict the relevance between a new item i for user u, memory-based filtering provides an aggregation function based on user's historical ratings and can be written as,

relevance u,i = aggregate u ′ ∈N eighbor(u) rating u ′ ,i (6.7)
where N eighbor(u) is the set of users that are most similar to user u.

The selection of function aggregate is varied and here we give a few formulations,

relevance(u, i) = 1 |N eighbor(u)| u ′ ∈N eighbor(u) rating u ′ ,i (6.8) relevance(u, i) = 1 u ′ ∈N eighbor(u)
sim(u, u ′ ) u ′ ∈N eighbor(u) sim(u, u ′ ) * rating u ′ ,i (6.9)

relevance(u, i) =rating u + 1 u ′ ∈N eighbor(u) sim(u, u ′ ) u ′ ∈N eighbor(u) * sim(u, u ′ ) * (rating u ′ ,i -rating u ′ ) (6.10)
where sim(u, u ′ ) is a similarity measure between a pair of users u and u ′ and rating u represents the average rating score a user u gave the items. Eq. (6.8) is a simple average of all ratings of similar users regarding an item. Eq. (6.9) is an extended version of Eq. (6.8) by including the similarity between users as weight to differentiate the influence of users. And Eq. (6.10) further extends Eq. (6.9) by weighing in average rating scores of users to consider user related score scale difference.

So the essential task for memory-based CF approaches is an appropriate solution of finding similar users for each user. Mean Squared Difference (MSD), Pearson Coefficient and Cosine Similarity have been employed for this purpose to calculate similarity of users based on co-rated items. We represent the co-rated items between a pair of users u and u ′ as CoR u,u ′ = {i|i ∈ I, ∃rating u,i ∃rating u ′ ,i }. For mean squared difference, the similarity between two users u and u ′ is given as,

sim M SD = i∈CoR u,u ′ (rating u,i -rating(u ′ , i)) 2 (6.11)
And Pearson coefficient for calculating the user similarity can be written as,

sim P earson = i∈CoR u,u ′ (rating u,i -rating u )(rating u ′ ,i -rating u ′ ) i∈CoR u,u ′ (rating u,i -rating u ) 2 i∈CoR u,u ′ (rating u ′ ,i -rating u ′ ) 2 (6.
12)

The cosine similarity on the other hand is given as,

sim cos = i∈CoR u,u ′ rating u,i * rating u ′ ,i i∈CoR u,u ′ (rating u,i ) 2 i∈CoR u,u ′ (rating u ′ ,i ) 2 (6.13)
GroupLens proposes in [START_REF] Resnick | Grouplens: An open architecture for collaborative filtering of netnews[END_REF] an architecture using Pearson coefficient and the a relevance given in Eq. (6.9) for generating personalized items to users. And Ringo is another memory-based CF approach proposed in [START_REF] Shardanand | Social information filtering: Algorithms for automating "word of mouth[END_REF] and has employed mean square difference and Pearson coefficient for finding similar users and predicting recommendation items. In [START_REF] Breese | Empirical analysis of predictive algorithms for collaborative filtering[END_REF] they have used both Pearson coefficient and cosine similarity with relevance function shown in Eq.(6.10) for making memory-based recommendation. Memory-based collaborative filtering relies heavily on finding similar users with similarity calculations |U | × |I| in total, which becomes expensive and time-consuming for scaling up. Some techniques [START_REF] Yu | Instance selection techniques for memory-based collaborative filtering[END_REF] to prune the user profiles first before the similarity calculations thus have been proposed. In [START_REF] Yu | Instance selection techniques for memory-based collaborative filtering[END_REF] they propose four different approaches to filter user profiles, accordingly by selecting new user profiles, rational user profiles, both new and rational profiles and user profiles with high utility score. By applying these approaches, the recommendation has been accelerated because of the reduction of calculating size whiling slightly improve the recommendation accuracy. Delgado et al. have argued that the proposed similarity functions shown as Eq. (6.11), (6.12) and (6.13) have no well founded theory and that learning weights through a combination of memory-based individual predictions and online weight-majority voting to replace the similarity is a better solution.

All the memory-based filtering methods above use aggregation function based on neighboring users' rating data, however, [START_REF] Sarwar | Item-based collaborative filtering recommendation algorithms[END_REF] and [START_REF] Deshpande | Item-based top-<i>n</i> recommendation algorithms[END_REF] replace the aggregation of ratings of similar user with aggregation of ratings of similar items. Thus to suit to change, the generic relevance function will be modified based on Eq.(6.7), written as,

relevance u,i = aggregate i ′ ∈Iu rating u,i ′ (6.14)
where I u is a list of N items that are most coarsely most relevant to the given user u. To obtain this list of items for each users, either a direct selection on rated items can be used or the similarity between the candidate items and rated items can be calculated and a top-N item list can be returned. The similarity function between candidate items and rated items can take form of aforementioned similarity metrics, namely, mean squared difference, Pearson coefficient and cosine similarity. An example of similarity functions for two items i and i ′ based on co-rating history are given as such. For a Pearson coefficient-based item similarity, it is written as,

sim P earson = u∈CoR i,i ′ (rating u,i -rating i )(rating u,i ′ -rating i ′ ) u∈CoR i,i ′ (rating u,i -rating i ) 2 u∈CoR i,i ′ (rating u,i ′ -rating i ′ ) 2 (6.15)
where CoR(i, i ′ ) is the set of users who have co-rated the two items. Then by applying Eq.(6.14), a refined and final item list for each user can be returned by sorting the relevance between user u and item i. Empirical results have shown a better performance compared to user memory-based collaborative filtering approaches. Despite memory-based collaborative filtering methods have overcome some limits of content-based filtering, e.g. being able to provide quality-measured items to users and empirical results have shown certain success, there are still major shortcomings, namely, -Memory-based collaborative filtering requires to calculate for each item a similarity function involved with a big chunk of all data to generating the recommendation. In consequence it presents serious scalability problems when applying memory-based methods. Particularly in online recommendation scenarios which are expected with short-time response, a memory-based CF would require complicated infrastructure to provide sufficient service.

-Memory-based collaborative filtering relies directly on historical co-rating data for a pair of users or co-rated data for a pair of items, which in reality is highly scarce. That being said, each user only rates a small subset of total items, giving very little information for user item relevance calculation. And furthermore, even only considering users who have historically rated at least a fixed number of items and items which have been at least rated for a minimum times, the overlap of co-rated items or co-rating users will still present small in general. Therefore, based on only a few observations of correlation data (co-rating users or co-rated items), the computed relevance should not be considered as a reliable measure [START_REF] Billsus | Learning collaborative information filters[END_REF]. Besides, it is inevitable that memory-based collaborative filtering approaches will perform much worse when datasets present high sparsity.

-Memory-based collaborative filtering only considers the neighboring rating data of users or items, but it has been argued that ratings given by a user can still be useful to another user even if the user is not in another user's neighborhood [START_REF] Billsus | Learning collaborative information filters[END_REF].

Regarding these limits, model-based collaborative filtering methods have been proposed to partially alleviate the problems. And we give a more detailed introduction in next subsection.

Model-Based Collaborative Filtering

Model-based collaborative filtering approaches [START_REF] Billsus | Learning collaborative information filters[END_REF][START_REF] Goldberg | Eigentaste: A constant time collaborative filtering algorithm[END_REF][START_REF] Rendle | Bpr: Bayesian personalized ranking from implicit feedback[END_REF][START_REF] Kabbur | Fism: Factored item similarity models for top-n recommender systems[END_REF][START_REF] Wang | Irgan: A minimax game for unifying generative and discriminative information retrieval models[END_REF] also use historical rating data to recommend items that are preferred by other users with similar tastes. But instead of calculating the relevance directly with rating data, model-based CF methods build or learn a model first and the recommendation will be generated using this model under fewer calculations compared to memory-based CF. Various models from pattern recognition and machine learning tasks have been employed for recommendation, taking examples as Singular Value Decomposition [START_REF] Billsus | Learning collaborative information filters[END_REF], Principal Component Analysis [START_REF] Goldberg | Eigentaste: A constant time collaborative filtering algorithm[END_REF], Matrix Factorization [START_REF] Salakhutdinov | Probabilistic matrix factorization[END_REF][START_REF] Rendle | Bpr: Bayesian personalized ranking from implicit feedback[END_REF] and Neural Networks [START_REF] Wang | Irgan: A minimax game for unifying generative and discriminative information retrieval models[END_REF].

Figure 6.3: A binarized rating matrix where each column represents the rating scores an item receives and each row represents the rating scores a user gives. The rating score 1 means a positive preference or like between a pair of user and item; and 0 means a negative preference or dislike between a pair of user and item. A '?' for rating score means no historical rating of this pair of user and item.

The historical rating data can be represented as a rating matrix, demonstrated in Fig. 6.3, and is in general highly sparse. The recommendation of items towards each user can be simplified as predicting the unknown rating score (either 1 or 0) and return the list of items with score 1 as final results. If we consider each user's preference (like and dislike) as a feature then the prediction problem is a typical classification problem in machine learning. However, the dimension of features is proportional to the number of users which may suffer from the curse of dimensionality [START_REF] Hammer | Adaptive control processes: A guided tour (r. bellman)[END_REF] when the user count is too big. In the mean time, if treating unknown rating score as negative (which is a common practice during training procedure), each item's feature vector is mostly composed of 0 and thus also highly sparse. Some methods [START_REF] Billsus | Learning collaborative information filters[END_REF][START_REF] Goldberg | Eigentaste: A constant time collaborative filtering algorithm[END_REF] are therefore inspired by dimensionality reduction solutions in machine learning for this classification. D. Billsus et al. [START_REF] Billsus | Learning collaborative information filters[END_REF] presented a recommendation based on Singular Value Decomposition (SVD). For a rectangular matrix A ∈ R b×c with rank m, SVD can decompose it into the product of three matrices,

A = U ΣV ⊤ (6.16)
where U and V are orthonormal vectors and Σ is a diagonal matrix containing the singular values. In their proposal, all the feature vectors of items compose a new rectangular matrix where SVD can be applied to obtain singular values which can rescale the feature vectors for prediction. Eigentaste [START_REF] Goldberg | Eigentaste: A constant time collaborative filtering algorithm[END_REF] is another dimensionality reduction-based recommendation where Principal Component Analysis (PCA) is applied on the item correlation matrix to get a fix number of eigen vectors for an 'eigen-plane'. The eigen-plane can be used to map rating matrix into lower continuous space for clustering and then generation of recommendation lists.

Matrix Factorization (MF) is another category of model-based CF methods where a rating matrix is directly learnt to map into a low-rank matrix and recommendation can be inferred from the low-rank matrix. Given a rating matrix M , Funk matrix factorization [55] proposes to predict the rating matrix M by learnt item latent vectors V I ∈ R |I|×d and user latent vectors V U ∈ R |U |×d by a matrix multiplication operation,

M = V U V ⊤ I (6.17)
To learn the item latent vectors and user latent vectors,

loss : arg min V U ,V I ∥M -M ∥ 2 + λ 1 ∥V U ∥ 2 + λ 2 ∥V I ∥ 2 (6.18)
where λ 1 and λ 2 are parameters for model regularization. SVD++ [START_REF] Koren | Factorization meets the neighborhood: A multifaceted collaborative filtering model[END_REF] is another matrix factorization-based model which also incorporates a neighborhood model, which considers both explicit feedback Rating expl and implicit feedback Rating impl , written as

M u,i = b u,i + V ⊤ i ( j∈Rating expl (u) (M u,j -b u,j )x j + |Rating impl (u)| -1/2 j∈Rating impl (u)) y j ) (6.19)
where M u,i is the element of row u and column i in M , M u,i is the element of row u and column i in M , V i is the i-th row vector in V I . b i,j is the bias vector for the pair of user u and item i. x j and y j are parameters to be learned for weighing different items. To accommodate the modification of the prediction of M the loss function is also modified accordingly, written as, loss :arg min

V I ,x * ,y * ,b * (u,i) (M u,i -b u,i -V ⊤ i ( j∈Rating expl (u) (M u,j -b u,j )x j + 1 |Rating impl (u)| j∈Rating impl (u)) y j )) 2 + λ(V 2 u + V 2 i + b 2 u,i + j x 2 j + j y 2 j ) 2 (6.20)
PMF [START_REF] Salakhutdinov | Probabilistic matrix factorization[END_REF] is also a matrix factorization-based CF method, where probabilistic graphical models are introduced to restrain the item latent vectors, user latent vectors and predicted rating matrix. The item, user latent vectors and predicted rating matrix are assumed to follow the Gaussian distribution, and the loss function is therefore the posterior distribution over users and items, written as,

loss : ln p(V U , V I |M, σ, σ U , σ V ) =∥M -M ∥ 2 + λ 1 ∥V U ∥ 2 + λ 2 ∥V I ∥ 2 (6.21)
All the matrix factorization-based methods above all optimize an element-wise RSME loss function with regard to the true explicit/implicit feedback of a pair of user and item. The choice of such a loss function corresponds to a regression/classification problem. However, item recommendation especially top-N recommendation is preferred to be regarded as a personalized ranking problem. Therefore to directly optimize a ranking a generic optimization criterion BPR-OPT is proposed in [START_REF] Rendle | Bpr: Bayesian personalized ranking from implicit feedback[END_REF]. The BPR-OPT criterion is given as,

BP R -OP T . = ln p(Θ| > u ) = (u,i,j) ln σ( x u,i,j ) + λ Θ ∥Θ∥ 2 (6.22)
where Θ is the set of parameters in a model, σ is the sigmoid function and > u represents the preference (ranking) structure for a user u. The triple (u, i, j) is preference structure for user u with items i and j.

FISM [START_REF] Kabbur | Fism: Factored item similarity models for top-n recommender systems[END_REF] is also based on matrix factorization but adds a discount factor for the item and user latent vector multiplication. Besides, FISM applies both RMSE loss and the BPR-OPT criterion for parameter learning, and empirical results show a more stable result given by BPR-OPT criterion.

IRGAN [START_REF] Wang | Irgan: A minimax game for unifying generative and discriminative information retrieval models[END_REF] applies a minimax game to the matrix factorization-based CF. Inspired by Generative Adversarial Nets (GAN) [START_REF] Goodfellow | Generative adversarial nets[END_REF], IRGAN is composed of a generative retrieval model (G) and discriminative retrieval model (D) which both are a matrix factorizationbased CF model. The overall loss function for learning the generative and discriminative models is by a minimax optimization, written as,

J G,D . = min θ max ϕ u∈U [E i∼ptrue(i|u,Rating) [log σ(f ϕ (u, i))]+ E i∼p θ (i|u,Rating) [log(1 -σ(f ϕ (u, i)))]] (6.23)
where the generative model tries to estimate the real relevance distribution for user u towards item i as a conditional probability p true (i|u, Rating) given the historical useritem interactions Rating, and is denoted as G(i|u) = p θ (i|u, Rating). The discriminative model D models and optimizes the probability of item i is preferred by user u, written in the sigmoid function

D(i|u) = σ(f θ (u, i)).
And both the generative model G(i|u) and discriminative model D(i|u) in item recommendation setting are score functions of matrix factorization-based methods, given as,

G(i, u) = σ(s θ (u, i)) = σ(b θ i + v θ⊤ u v θ i ) D(i, u) = σ(s ϕ (u, i)) = σ(b ϕ i + v ϕ⊤ u v ϕ i ) (6.24)
Model-based collaborative filtering methods have been reported to have a better performance than memory-based collaborative filtering methods [START_REF] Breese | Empirical analysis of predictive algorithms for collaborative filtering[END_REF] and can alleviate the sparsity problem to some degree. However, with emerging issues such as cold start problems [START_REF] Lam | Addressing coldstart problem in recommendation systems[END_REF] which means the difficulty of handling new users with very few historical interactions with items or new items in the recommender system, new techniques are proposed through combining various types of recommendations to maximize the benefits of their advantages while limiting the disadvantages. These new techniques are categorized as hybrid recommender systems.

Hybrid Recommender Systems

As content-based filtering and collaborative filtering both have their own advantages and disadvantages, it is natural to think of combining the two methods for benefiting from the advantages while avoiding the weakness. Thus, various types of hybrid recommender systems (weighted [START_REF] Claypool | Combining content-based and collaborative filters in an online newspaper[END_REF], switching [START_REF] Billsus | User modeling for adaptive news access[END_REF], mixed [START_REF] Smyth | A personalised tv listings service for the digital tv age[END_REF], feature combination [START_REF] Basu | Recommendation as classification: Using social and content-based information in recommendation[END_REF], feature augmentation [START_REF] Derry | Preserving recommender accuracy and diversity in sparse datasets[END_REF], cascade, meta-level [START_REF] Balabanović | Fab: Content-based, collaborative recommendation[END_REF]) have been proposed incorporating the two for achieving a more satisfying result [START_REF] Burke | Hybrid Web Recommender Systems[END_REF].

In [START_REF] Claypool | Combining content-based and collaborative filters in an online newspaper[END_REF] they propose to compute a weighted score for final recommendation from separate CF and CBF learning components. NewsDude [START_REF] Billsus | User modeling for adaptive news access[END_REF] is a switching-based hybrid method which chooses between CF and CBF recommendation for the final recommendation. In mixed hybrid method [START_REF] Smyth | A personalised tv listings service for the digital tv age[END_REF], recommendation results from different recommendation components are mixed and presented together to the users. The feature combination-based hybrid method [START_REF] Basu | Recommendation as classification: Using social and content-based information in recommendation[END_REF] exploits features from various sources and combines them together to train a single recommendation model. While feature augmentation-based method [START_REF] Derry | Preserving recommender accuracy and diversity in sparse datasets[END_REF] takes existed features to compute new features and use the new features as input for generating recommendation. Fab [START_REF] Balabanović | Fab: Content-based, collaborative recommendation[END_REF] proposes a meta-level hybrid system by maintaining both user profiles based on content analysis (CBF task) and comparing profiles to find similar users (memory-based CF task) at the same time. The recommendation generation will be a merge of the two recommendation results.

Knowledge Graph Embedding and KGE Based Recommendation

In previous chapter, we have seen several traditional recommendation techniques, using item textual content information, or user-item interactions or both. Empirical results have shown that using different sources of information from recommendation scenarios tend to boost recommendation. Hybrid methods have benefited from this combination of information but the way of traditional hybrid methods are in general either a simple aggregation of the two other methods lacking a more general and unified structure or too expensive and time consuming. Thus, given various kinds of information (user-item interactions, item-side auxiliary information etc) new approaches based on knowledge graph embedding have been proposed.

Knowledge graph embedding methods focus on learning latent representations of elements on knowledge graph. A knowledge graph is a graph-based data model, containing entities (vertices on the graph) and relations (links) connecting the entities for integrating knowledge and information. Various methods have been proposed to map knowledge graphs in latent vector spaces. The applications to link prediction, triple classification, entity recognition, clustering etc. have been proved to be successful in both academic works and industry.

A formal definition of a knowledge graph is given as such.

Definition 1.

A knowledge graph G = {E, R, T } is a set of entities E, relations R and triplets T . A triplet T is represented as (h, r, t) where h ∈ E is the head entity, t ∈ E is the tail entity and r ∈ R is the relation of the triplet. We denote ζ as the set of all correct combinations of triplets given E and R. And the triplets T in the knowledge graph G is a subset of ζ.

In Figure 7.1 we demonstrate a simple example of knowledge graph embedding for part of MovieLens data. In this example, the triplets of the knowledge graph shown on the left are listed as follows: And all the entities and relations shown in the In this section we first introduce three main categories of prevalent knowledge graph embedding techniques: the tensor decomposition based knowledge graph embedding, translation based knowledge graph embedding and the most recent deep neural network based graph embedding. We then present the state-of-the-art methods for incorporating knowledge graph embedding methods for enhancing recommendation performance. entities (movies, staff working for the movies, genres) and relations connecting the entities (InActorOf, IsInGenre etc.). On the right it is the latent embedding space where both entities and relations are embedded into. Knowledge graph embedding methods map elements of a knowledge graph (including both entities and relations) into the latent space while conserving the graph structure(node similarity etc.).

Tensor Decomposition Based Knowledge Graph Embedding

Tensor decomposition based knowledge graph embedding methods are a group of methods using decomposed matrices to represent knowledge graph triplet information. That is to say the score function for measuring a triplet (h, r, t) is based on multiplications of matrices of entity and relation vectors. RESCAL [START_REF] Nickel | A three-way model for collective learning on multi-relational data[END_REF], DisMult [START_REF] Yang | Embedding entities and relations for learning and inference in knowledge bases[END_REF], SimplE [START_REF] Mehran | Simple embedding for link prediction in knowledge graphs[END_REF], ComplEx [START_REF] Trouillon | Complex embeddings for simple link prediction[END_REF] are typical bilinear tensor decomposition based knowledge graph embedding methods; and HolE [START_REF] Xue | Expanding holographic embeddings for knowledge completion[END_REF] and TuckerER [START_REF] Balazevic | TuckER: Tensor factorization for knowledge graph completion[END_REF] are other linear tensor decomposition based knowledge graph embedding methods.

RESCAL [START_REF] Nickel | A three-way model for collective learning on multi-relational data[END_REF] incorporates a tensor factorization model to represent the translation from entity h to entity t through relation r, and the score function of the triplet (h, r, t)is formulated as,

score RESCAL (h, r, t) : v ⊤ h M r v t (7.1)
where M r ∈ R d×d is the square matrix that models the interaction between entities and v h ∈ R d and v t ∈ R d are entity vectors for h and t separately. And d is the latent dimension for the embedding. We also point out that this square matrix M r is by default asymmetric, which means the relation between a pair of entities does not have to be symmetric.

DistMult [START_REF] Yang | Embedding entities and relations for learning and inference in knowledge bases[END_REF] proposes to interact the relation vector r with the entity h and t in an element-wise multiplication way, and the score function of DistMult for the triplet (h, r, t)

is formulated as, score DistM ult : (v h ⊙ v r ) ⊤ v t (7.2)
where v h ∈ R d ,v r ∈ R d ,and v t ∈ R d are embedded vectors for h ,r and t correspondingly and ⊙ is the element-wise (Hadmard product) multiplication operator. We can easily tell the relation parameter size (R d ) is much smaller than that of RESCAL (R d×d ). Though as the score function does not distinguish between head and tail entities, DistMult can only model symmetric relations.

ComplEx [START_REF] Trouillon | Complex embeddings for simple link prediction[END_REF] confirms the effectiveness of dot product as the score function in knowledge graph embedding but it argues that extending real-valued vectors to complex-valued vectors will make the embedding more expressive while maintain a low parameter size. Thus, ComplEx uses a complex eigen decomposition form for representing the score function, formulated as,

score ComplEx : Re(v ⊤ h w r v t ) (7.3)
where

v h ∈ C d , v t ∈ C d ,
score ComplEx =Re(v ⊤ h w r v t ) =Re( d j=1 v hj * w rj * v tj ) =Re[ d j=1 (Re(v h ) + Im(v h )i) * (Re(v r ) + Im(v r )i) * (Re(v t ) + Im(v t )i)] = d j=1 [Re(v hj ) * Re(v rj ) * Re(v tj ) + Im(v hj ) * Re(v rj ) * Im(v tj ) + Re(v hj ) * Im(v rj ) * Im(v tj ) -Im(v hj ) * Im(v rj ) * Re(v tj )] =⟨Re(v h ), Re(v r ), Re(v t )⟩ + ⟨Im(v h ), Re(v r ), Im(v t )⟩+ ⟨Re(v h ), Im(v r ), Im(v t )⟩ -⟨Im(v h ), Im(v r ), Re(v t )⟩ (7.5)
where ⟨v, w, x⟩ . = d j=1 v j * w j * x j and v j ,w j and x j represents the j-th element of the corresponding vectors v,w and x.

SimplE [START_REF] Mehran | Simple embedding for link prediction in knowledge graphs[END_REF] exploits another decomposition -the canonical Polyadic (CP) decomposition for knowledge graph embedding usage. Here, each entity e is represented as two vectors h e and h t instead of one single vector, and each relation r is represented as two vectors v r and v v -1 . For a triplet (e 1 ,r,e 2 ), the similarity function is ⟨h e 1 , v r , t e 2 ⟩; while if we reconsider the reverse of this triplet (e 2 , r -1 , e1), the similarity function is ⟨h e 2 , v r -1 , t e 1 ⟩. And the translation function for two entities e 1 and e 2 related by relation r is defined as,

score SimplE : 1 2 (⟨h e 1 , v r , t e 2 ⟩ + ⟨h e 2 , v r -1 , t e 1 ⟩) (7.6)
which is the averaged similarities for (e 1 ,r,e 2 ) and (e 2 , r -1 , e 1 ).

HolE [START_REF] Xue | Expanding holographic embeddings for knowledge completion[END_REF] uses instead of multiplication operators a compositional operator -holographic operator which captures the idea of circular correlation. Given two vectors u and v, a holographic compositional operator hol :

R d × R d → R d is defined as hol(u, v) = u ⋆ v = [h 1 (u, v), ..., h k (u, v), ..., h d (u, v)] where, h k (u, v) = [u ⋆ v] k = d-1 j=0 u i v (i+k)modd (7.7)
thus, the score function for a triplet (h, r, t) in holographic embedding is given as,

score HolE : (v h ⋆ v t ) • v r (7.8)
And in practice, the holographic operator can be efficiently calculated with fast Fourier Transform (FFT), denoted as hol(u, v) = F -1 (F(u) ⊙ F(v)), where ⊙ represents the element-wise product, F represents the discrete Fourier transform and (x) represents the complex conjugate of x. Thus, the score function Eq. 7.8 can be rewritten as,

score HolE : v ⊤ r (F -1 (F(v h ) ⊙ F(v t ))) (7.9) ,denoted as hol(u, v) = F -1 (F(u) ⊙ F(v)).
TuckerER [START_REF] Balazevic | TuckER: Tensor factorization for knowledge graph completion[END_REF] is another linear model which is based on Tucker decomposition. Given an original matrix X ∈ R I×J×K , Tucker decomposition transforms the original matrix into a core tensor Z ∈ R P ×Q×R and three other matrices

A ∈ R I×P ,B ∈ R J×Q , C ∈ R K×R , formalized as, X = Z × 1 A × 2 B × 3 C (7.10)
where × 1 ,× 2 and × 3 are tensor products along the n-th mode, n = 1, 2, 3. The n-th mode tensor product of Z by A(or B or C) is denoted as

Z × 1 A (or Z × 2 B or Z × 3 C) with entries of each formulated as, (Z × 1 A)(x 1 , x 2 , x 3 ) = P i 1 =1 Z(i 1 , x 2 , x 3 )A(x 1 , i 1 ) (Z × 2 B)(x 1 , x 2 , x 3 ) = Q i 2 =1 Z(x 1 , i 2 , x 3 )B(x 2 , i 2 ) (Z × 3 C)(x 1 , x 2 , x 3 ) = R i 3 =1 Z(x 1 , x 2 , i 3 )C(x 3 , i 3 ) (7.11)
where x 1 , x 2 , x 3 ∈ R are entry indexes of each dimension. The dimensions P, Q, R of core tensor Z are smaller than the dimensions I, J, K, thus Tucker decomposition can be considered a compressed version of X. Based on all these, TuckerER defines the score function for a triplet (h, r, t) as, As for loss functions for the learning process, both penalized itemwise and pairwise loss functions are used for different tensor decomposition based knowledge graph embedding. For RESCAL, as the score function is formulated as 7.1, they employ a penalized squared loss represented as such,

score T uckerER : W × 1 v h × 2 v r × 3 v t (7.12) where v h , v t ∈ R de , v r ∈ R dr , W ∈ R
loss RESCAL . = k ∥Y k -V E M r k V ⊤ E ∥ 2 F + λ 1 ∥V E ∥ 2 F + λ 2 k ∥M r k ∥ 2 F (7.13)
where λ 1 and λ 2 are the regulation parameters and Y k is the label vector corresponding to the k-th relation.

ComplEx, SimplE, HolE and TuckerER share a same penalized loss function but they have employed a negative log-likelihood of the logistic model in their form. The general form of this loss function can be written as such,

loss log l ogistic . = (h,r,t) log(1 + e ( -Y h,r,t ϕ(h, r, t, Θ))) + λ∥Θ∥ 2 2 (7.14)
where Θ represents all the learnable parameters (latent vectors) and ϕ(h, r, t, Θ) is the score function for the triplet (h, r, t). λ is the regulation parameter. DistMult on the other hand uses a margin-based loss function shared with translation-based knowledge graph embedding methods. And we will give the margin-based loss function in the next section. A translation-based knowledge embedding basically considers a semantic translation from one entity (head, h) to another entity (tail, t) by a specific relation r, i.e. v h + v r ≈ v t when the triplet (h, r, t) holds. Different translation-based models [START_REF] Bordes | Translating embeddings for modeling multi-relational data[END_REF][START_REF] Wang | Knowledge graph embedding by translating on hyperplanes[END_REF][START_REF] Ji | Knowledge graph embedding via dynamic mapping matrix[END_REF][START_REF] Lin | Learning entity and relation embeddings for knowledge graph completion[END_REF] vary in the projected low-dimensional continuous space of entities and relations.

Translation Based Knowledge Graph Embedding

TransE [START_REF] Bordes | Translating embeddings for modeling multi-relational data[END_REF] maps both relations and entities lay on the same space and represents the translation function of a triplet (h, r, t) simply as,

translation T ransE : ∥v h + v r -v t ∥ 2 (7.15)
where v h , v r , v t ∈ R d are latent vectors for h, r and t separately.

TransH [START_REF] Wang | Knowledge graph embedding by translating on hyperplanes[END_REF] however projects the entities to a hyperplane by a norm vector w r ∈ R d for each type of relation first then considers the projected entities and original relations on the same latent space. For entities h and t, after being projected to a hyperplane noted by its direction vector w r corresponding to the relation r, they are written as

v h ⊥ = v h -w ⊤ r v h w r , v h ⊥ ∈ R d and v t ⊥ = v t -w ⊤ r v t w r , v t ⊥ ∈ R d separately,
thus the translation for TransH can be written as,

translation T ransH . =∥v h ⊥ + v r -v t ⊥ ∥ 2 =∥(v h -w ⊤ r v h w r ) + v r -(v t -w ⊤ r v t w r )∥ 2 (7.16)
By mapping entities to a relation-related hyperplane, TransH improves performance compared to TransE over link prediction, node classification and other common knowledge embedding applied tasks, while the training parameter size is also slightly increased. In Figure 7.2 we give simple illustrations of TransE and TransH on latent space.

TransR [START_REF] Lin | Learning entity and relation embeddings for knowledge graph completion[END_REF] projects entities and relations to separate spaces through a relational projection matrix M r ∈ R d×d . Thus the translation for TransR can be written as,

translation T ransR : ∥v h M r + v r -v t M r ∥ (7.17)
TransD [START_REF] Ji | Knowledge graph embedding via dynamic mapping matrix[END_REF] also projects entities to separate spaces but comparing to TransR, TransD uses a dynamic mapping matrix for each entity. That is to say, for each triplet (h, r, t), we also have entity-related project vector h p ∈ R d and t p and relation-related project vector r p ∈ R d and the dynamic mapping matrices for h and t are defined correspondingly as,

M rh = r p h ⊤ p + I (7.18) M rt = r p t ⊤ p + I (7.19)
where I ∈ R d×d is the identity matrix having the same dimensions as r p h ⊤ p . And the translation function for TransD can be written as,

translation T ransD . = ∥v h M rh + v r -v t M rt ∥ (7.20)
By comparing the two equations Eq.(7.17) and Eq.(7.20), there is high similarity in translation definition as entities h and r are both transformed through a mapping matrix before applying the simple translation form. However, the difference lies in the fact that in TransD, as the mapping matrix is dynamic and is decomposed into r p ∈ R d and e p ∈ R d , the size of trainable parameter are greatly reduced compared to an unknown matrix M r ∈ R d×d . In Figure 7.3 we give a simple illustration of TransD, mapping from entity space to relation space.

TransE, TransH, TranR and TransD all have employed ∥ • ∥ 2 a euclidean metric for the definition of translation function. TransA [START_REF] Xiao | Transa: An adaptive approach for knowledge graph embedding[END_REF], however, argues that by replacing this oversimplified euclidean metric by a more flexible Mahalanobis distance, the translation of a triplet (h, r, t) can be expressed in a more adaptive way thus gaining in performance.

The translate function of TransA is given as such,

translation T ransA . = (∥v h + v r -v t ∥ ⊤ )W r (∥v h + v r -v t ∥) (7.21)
where W r ∈ R d×d is a relation-related non-negative weighted matrix corresponding to the adaptive distance.

In order to learn the entity/relation vectors and projection vector/matrix, translationbased knowledge graph embedding employs a margin-based pairwise loss function based on score function f r (h, t), which refers to different translation functions simulating the idea of v h + v r ≈ v t . The margin-based ranking loss is optimized to distinguish golden triplets T (those hold under historical interactions) and incorrect triplets T ′ (those unhold under historical interactions or unknown triplets), and is written as,

loss KGE . = (h,r,t)∈T (h ′ ,r ′ ,t ′ )∈T ′ [f r (h, t) + γ -f r ′ (h ′ , t ′ )] + (7.22)
where (h ′ , r ′ , t ′ ) is a negative triplet degenerated from the golden triplet (h, r, t) and γ is the margin parameter. [x] + is absolute value of x.

Compared to tensor decomposition based knowledge graph embedding methods, translationbased knowledge graph embedding usually exhibit simpler forms and less complicated operations, while works have reported better performance of tensor decomposition based methods for complicated tasks (involving asymmetric relations and n-n relations).

Deep Neural Network Based Knowledge Graph Embedding

Deep neural networks have shown huge success in various machine learning (ML) domains, such as computer vision and natural language processing. Inspired by the successful applications in ML, works incorporating neural networks have been proposed by various researches for knowledge graph embedding learning. In neural network based knowledge graph embedding methods, entities and relations are still represented in latent vectors or tensors, while the score function for representing the relation of a triplet (h, r, t) is replaced with a neural network layer.

The Neural Tensor Network (NTN) [START_REF] Socher | Reasoning with neural tensor networks for knowledge base completion[END_REF] model proposes to use a bilinear tensor layer to relate two entity vectors before wrapping the unit in a non-linear activation function. And the score function of a triplet (h, r, t) is given as, Special types of deep neural networks have been developed in fascinating fashions and there is much spotlight on Convolutional Neural Networks (CNNs) particularly. Derived from CNNs, Graph Neural Networks (GCNs) [START_REF] Kipf | Semi-supervised classification with graph convolutional networks[END_REF] use multi-layer node embedding and spectral convolution on graphs to propagate the embedding between layers. The recent development in GCNs helps deep neural networks perform well in many tasks on graph structures. And it is natural to expand this line of work to knowledge graphs, and several works have been proposed for combining GCN in knowledge graph embedding.

score N T N . = u ⊤ r tanh(v ⊤ h W [1:k] r v t + V r   v h v t   + b r ) (7.23) where v h , v t ∈ R d , W [1:k] r ∈ R d×d×k
In vanilla GCN, each layer l of neural networks contains all the entities representations, and from layer l to layer l + 1, the propagation is given by the formula below, Inspired by Eq.7.24, CompGCN [START_REF] Vashishth | Compositionbased multi-relational graph convolutional networks[END_REF] propagates both entity and relation in each layer by using a composition operator relating the entity and relation vectors. And the propagation from layer l to l + 1 for an entity e is given as such,

v l+1 e = σ(W l (m l+1 e + v l e )) ( 7
v l+1 e = σ(m l+1 e + W l 0 v l e ) (7.26)
where m l+1 e is related to relation r and written as,

m l+1 e = (e ′ ,r)∈N in (e) W l r ϕ in (v l e ′ , v l r ) + (e ′ ,r)∈Nout(e) W l r ϕ out (v l e ′ , v l r ) (7.27)
where ϕ in , phi out : R d l × R d l → R d l are the composition operators corresponding to entity e as tail or head in the triplet, and v l r is propagated as, [START_REF] Borodin | Max-sum diversification, monotone submodular functions, and dynamic updates[END_REF] where f in and f out are the score function used in non-DNN based knowledge graph embedding. In a similar fashion the relation vector is propagated from layer l to l + 1 as such,

v l+1 r = W l rel v l r (7.28) W l 0 , W l r , W l rel ∈ R d l ×d
m l+1 e = (e ′ ,r)∈N in W l r ∂f in (v l e ′ , v l r , v l e ) ∂v l e + (e ′ ,r)∈Nout W l r ∂f out (v l e , v l r , v l e ′ ) ∂v l e (7.
v l+1 r = σ rel (W l rel (m l+1 r + v l r )) (7.31)
and m l+1 r is given as,

m l+1 r = (e,e ′ )∈N (r) ∂f r (v l e , v l r , v l e ′ ) ∂v l r (7.32)
In terms of loss functions for deep neural network based knowledge graph embedding, both margin-based ranking loss function in Eq. (7.22) and log logistic loss function Eq. (7.14) are used for different tasks. We point out that in GCN-based knowledge graph embedding, the score function for a triplet (h, r, t) is simply given as,

f (h, r, t) = ∥v h -v t ∥ (7.33)
as v h and v t are updated at each layer through a relation-related form as in Eq.(7.29) and Eq.(7.31).

KGE-Based Recommendation

We have seen in previous sections different models of knowledge graph embedding methods, employing various score functions to capture structured knowledge information. Having witnessed the success in other ML tasks such as node classification and link prediction, and based on assumption that auxiliary information may be used to enhance the performance of recommendation, many works [START_REF] Zhang | Collaborative knowledge base embedding for recommender systems[END_REF][START_REF] Xin | Relational collaborative filtering: Modeling multiple item relations for recommendation[END_REF][START_REF] Wang | Dkn: Deep knowledgeaware network for news recommendation[END_REF][START_REF] Wang | Ripplenet: Propagating user preferences on the knowledge graph for recommender systems[END_REF][START_REF] Ye | Bayes embedding (bem): Refining representation by integrating knowledge graphs and behavior-specific networks[END_REF][START_REF] Wang | Knowledge-aware graph neural networks with label smoothness regularization for recommender systems[END_REF] have been dedicated to incorporate knowledge graph embedding into recommender systems.

CKE [START_REF] Zhang | Collaborative knowledge base embedding for recommender systems[END_REF] leverages three types of information -structural content, textual content and visual content to jointly learn knowledge graph embedding and collaborative filtering representations. More particularly, for processing structural content composed of knowl-edge triplets (head, relation, tail), the probabilistic translation-based knowledge graph embedding TransR [START_REF] Lin | Learning entity and relation embeddings for knowledge graph completion[END_REF] with a log logistic loss function is applied, which also helps the construction of item latent vector.

Deep knowledge-aware network (DKN) [START_REF] Wang | Dkn: Deep knowledgeaware network for news recommendation[END_REF] is a content-based model which combines convolutional neural networks for textual information and knowledge graph embedding for structural contextual information forming a multi -channel and word -entityaligned representation for click-through rate (CTR) prediction. DKN also applies an attention network [START_REF] Bahdanau | Neural machine translation by jointly learning to align and translate[END_REF] after the representation embedding layer for further enhancing the prediction performance while accentuating more influencing contexts which leads to a certain prediction result.

RippleNet [START_REF] Wang | Ripplenet: Propagating user preferences on the knowledge graph for recommender systems[END_REF] is also a CTR prediction which implements preference propagation on the knowledge graph based KGE methods. More specifically, RippleNet first extracts k-click ripple sets defined as the set of triplets starting from (k -1)-click reachable entities. Then similar to a content-based filtering model, the user representation v u is the sum of all preferences reflected by k-click triplets and the predicted clicking probability of user u

toward item i is given as, ŷu,i = sigmoid(v ⊤ u v i ) (7.34)
RCF [START_REF] Xin | Relational collaborative filtering: Modeling multiple item relations for recommendation[END_REF] departs from item-based collaborative filtering (ICF) methods and jointly learns a user-item preference model and an item-item relational data model. And in user-item preference model, they propose a two-level hierarchy attention mechanism to capture the interactions between user embedding and relation types and the weights between users and historical items with specific relation values. The loss function for this ICF-based user-item preference model is given as,

loss rcf -rec . = - (u,i,k)∈D I ln sigmoid(M LP (m u,i ⊙ q i ) -M LP (m u,k ⊙ q j )) (7.35)
where M LP is a multilayer perceptron (MLP), D I is the triplet of user u, positive item i and negative item j, q i and q j are item embedding vectors for item i and item j separately.

m u,i and m u,j are user embedding vectors with the two-level hierarchy attention mechanism. And we give the formulation of the target-aware user embedding m u,i as such,

m u,i = p u + t∈T softmax(a(p u , x t )) • s t u,i (7.36)
where softmax(a(p u , x t )) is the first-level attention between user embedding p u and relation type embedding x t ; and s t u,i is the second-level attention between user and items in terms of specific relation values for each relation type. Besides, the item-item relational data models treats item auxiliary information as knowledge graph and applies DistMult [START_REF] Yang | Embedding entities and relations for learning and inference in knowledge bases[END_REF] for knowledge graph embedding. To link the user-item preference model and the item-item relational model together, the relation embedding vector v r in item-item relational model for relation type r is the combination of the relation type latent vector x t and relation value vector z v in user-item preference model and is written as v r = x t + z v . And the loss function of the item-item relational model is given as,

loss rcf -rel . = (h,r,t,t ′ )∈D R ln sigmoid(f r (h, t) -f r (h, t ′ )) (7.37)
where D R denotes a pair of triplets where (h, r, t) is the golden triplet in knowledge graph and (h, r, t ′ ) is the corresponding negative triplet.

BEM [START_REF] Ye | Bayes embedding (bem): Refining representation by integrating knowledge graphs and behavior-specific networks[END_REF] is an Bayesian approach of learning representations integrating knowledge graphs and behavior graphs for various knowledge graph tasks and item recommendation. BEM pre-trains separate embeddings for a knowledge graph (KG) and a behavior graph (BG) of a dataset with translation-based KGE methods, and then uses a bayesian framework to adjust the representations for both KG and BG representations. KGNN-LS [START_REF] Wang | Knowledge-aware graph neural networks with label smoothness regularization for recommender systems[END_REF] proposes a Label Smoothness regularization method to incorporate GCN-based knowledge graph embedding into recommendation.

Diversity-Aware Information Retrieval and Recommendation

Information retrieval (IR) [START_REF] Jansen | The seventeen theoretical constructs of information searching and information retrieval[END_REF] is a process to retrieve documents or information relevant to the demand, in forms of queries. A query is typically a piece of information (in texts, for example) given by the user to represent the characteristics or topics of potential information. Web search engines is one of the most common applications of information retrieval service on the Internet. Similar to recommender systems, the quality of rendering only relevant documents cannot fully achieve users' satisfaction due to the fact that the interpretation of a query can be vague and ambiguous. And focusing on maximizing one way of calculating the relevance between a query and the potential documents can lead to misunderstanding of users' intent or exposing too much redundant information. Thus, result diversification has been brought to IR to deal with this problem.

Recommendation problems, however, are highly similar to information retrieval in terms of goals both should attain to. Although in recommender systems, an explicit query in text or other formats is not given, it is expected to retrieve relevant items for each user by inferring from historical user behavior data and other available information. And as briefly presented in introduction, over-concentrating on predicting and returning relevant items deviates from the goal of maximizing user satisfactions. So it is essential to take diversity into account for achieving a better recommendation. In reality, due to a highly resembling goal shared by IR and recommendation, various methods for diversification in both areas have inspired one the other.

Because of the nature and their similarity of diversity related topics in information retrieval and recommendation, we present an overall view of works dedicated in diversityaware IR/recommendation in this section.

The roadmap of this section is that we will present the concept of diversity and its various definitions from different perspective. Then we will present various diversification methods proposed in existed works.

Diversity

Diversity has been brought up in information retrieval and recommender systems for over a decade due to various limits and issues reported in research works [START_REF] Ziegler | Improving recommendation lists through topic diversification[END_REF][START_REF] Pariser | The Filter Bubble: What the Internet Is Hiding from You[END_REF][START_REF] Nguyen | Exploring the filter bubble: The effect of using recommender systems on content diversity[END_REF][START_REF] Wu | Does diversity affect user satisfaction in image search[END_REF]. Despite the importance of diversity in IR and recommendation tasks, the definition of diversity in existent literature varies. As a matter of fact, the concept of diversity only refers to retrieving heterogeneous information or items [START_REF] Zanitti | A user-centric diversity by design recommender system for the movie application domain[END_REF], which leaves huge flexibility to researchers in academics and industry to define diversity differently according to the configuration required in various scenarios.

From the perspective of diversifying scale, diversity can be considered in either aggregated level or individual level. Aggregate diversity [START_REF] Vargas | Improving sales diversity by recommending users to items[END_REF][START_REF] Eskandanian | Using Stable Matching to Optimize the Balance between Accuracy and Diversity in Recommendation[END_REF][START_REF] Eskandanian | Using Stable Matching to Optimize the Balance between Accuracy and Diversity in Recommendation[END_REF] targets at improving a more balanced recommendation over all items towards users and alleviating the long-tail effect [START_REF] Sundaresan | Recommender systems at the long tail[END_REF][START_REF] Hongzhi Yin | Challenging the long tail recommendation[END_REF] as much as possible. The long-tail effect is a distribution with high occurrences that are far from the concentrated "head" and those high occurrences appear to be a long tail for such a distribution. And in Figure 8.1 we give an example of such effect. The latter actually reflects a systematic bias towards a huge quantity of items in IR or recommender systems and it is especially critical in retail business, where the aggregate diversity is named as sales diversity.

In contrast, individual diversity aims at providing a diversified personalized item list to each user to enhance personal experience and satisfactions of users in recommender systems. We focus on individual diversity in recommender systems in this thesis, thus we use simply the term diversity to refer to individual diversity in the following text.

A widely used definition of diversity in recommender systems and other information retrieval relies on semantic information, i.e. item categories [START_REF] Rakesh Agrawal | Diversifying search results[END_REF][START_REF] Vargas | Coverage, redundancy and size-awareness in genre diversity for recommender systems[END_REF][START_REF] Ashkan | Optimal greedy diversity for recommendation[END_REF] or tags/topics [START_REF] Nguyen | Exploring the filter bubble: The effect of using recommender systems on content diversity[END_REF][START_REF] Yue | Predicting diverse subsets using structural svms[END_REF][START_REF] Rodrygo | Exploiting query reformulations for web search result diversification[END_REF][START_REF] Szpektor | When relevance is not enough: Promoting diversity and freshness in personalized question recommendation[END_REF][START_REF] Zhu | Learning for search result diversification[END_REF]. The former assumes there is an existing taxonomy of information related to the retrieval/recommendation candidates, which serves to define or measure the returning diversity of results through relevance-related metrics. And the latter tends to use language models ( such as PLSA [START_REF] Hofmann | Probabilistic latent semantic analysis[END_REF], LDA [START_REF] Blei | Latent dirichlet allocation[END_REF]) to represent words or latent topics and based on that, the methods can use similarity/dissimilarity metrics for diversity purpose.

In [START_REF] Rakesh Agrawal | Diversifying search results[END_REF] the diversity corresponds to various intents of a given query, and is based on categorical information. Thus the measurement of result diversity relies on the probability of intent (category) of a query and the intent-dependent quality measure (NDCG,MRR,MAP), formulated as,

NDCG -IA(D, n) = c P (c|q)NDCG(D, n|c) MRR -IA(D, n) = c P (c|q)MRR(D, n|c) MAP -IA(D, n) = c P (c|q)MAP(D, n|c) (8.1)
where D is a list of document, n the cut-off number and c is a category or intent.

[84] also proposes a diversity measure based on categorical information. Inspired by binomial distribution, this diversity metric considers for each item i with its categories C(i) and a randomly sampled category c, whether c belongs to C(i) as an independent Bernoulli trial. And they model the probability of how adequate a genre c is covered in a top-N recommendation list, denoted as p c or P (X c ). Thus, they propose BinomDiv composed of two parts: Coverage(•) and N onRed(•), formulated separately as,

Coverage(D) = c / ∈C(D) P (X c = 0) 1/|C| (8.2) N onRed(D) = c∈C(D) P (X c >= k R c |X c > 0) 1/C(D) (8.3)
And finally BinomDiv is given as,

BinomDiv(D) = Coverage(D) • N onRed(D) (8.4)
Their diversity measure given in Eq.(8.4) considers both categorical coverage and redundancy, and measures the genre diversity of the recommended items assuming that the recommendation is the most diverse when its coverage of categories is proportional to categorical popularity in the system. In [START_REF] Ashkan | Optimal greedy diversity for recommendation[END_REF], they define their diversity function directly on categories, denoted as function f , given as,

f (D) = c∈C 1 {∃d ∈ D, d covers c} (8.5)
In [START_REF] Rodrygo | Exploiting query reformulations for web search result diversification[END_REF], the diversity measurement is not directly defined based on topical information. Rather, the item list diversity is evaluated as a redundancy estimation regarding the pre-selected relevant items, where the estimation is based on three language weighting methods. Given a query q and a set of pre-selected items D, the item list diversity at this iterative step for a document d is defined as,

P (d, D|q) = q i ∈Q P (q i |q)P (d, D|q i ) = q i ∈Q P (q i |q)P (d|q i )P (D|q i ) (8.6)
where q i is the sub-query of query q, Q is the collection of sub-queries corresponding to the original query q, and P (d|q i ) measures the coverage of document d with regard to sub-query q i and P (D|q i ) measures the novelty of the document d regarding q i .

[90] also does not define an explicit diversity metric but a utility function for a candidate item/document d over the original ranking results R q in terms of sub-queries, formulated as,

U (d|R q i ) = d ′ ∈Rq i 1 -cosine(d, d ′ ) rank(d ′ , R q i ) (8.7)
where q i is a specialized query (sub-query) of the original query q, and R q i corresponds to the ranking of documents given the sub-query q i . And the discounted factor 1-cosine(d, d ′ ) is the diversity consideration in this utility function for each new document d. [START_REF] Szpektor | When relevance is not enough: Promoting diversity and freshness in personalized question recommendation[END_REF] proposes to combine latent topics of textual information learnt from latent dirichlet analysis (LDA) [START_REF] Blei | Latent dirichlet allocation[END_REF] and category information as auxiliary information to build user profiles in question recommendation. The user profile actually is represented as a three level probability distribution tree, namely a top -category -distribution level, a modeldistribution level and a f eature -distribution level. The branches of such a tree structure correspond to the diverse intent recorded in the user profiles. In measuring the diversity both categorical information and LDA topics are considered to be covered. [START_REF] Zhu | Learning for search result diversification[END_REF] considers the diversity between a new document x i and pre-selected documents S as a relational function h S (•). This relational function takes various diversity feature vectors Div ij as input, and can be defined as the different distances between the new document x i and x j in pre-selected documents S. The different distances are namely Minimal Distance, Average Distance and Maximal Distance, formulated correspondingly as, h S (x i ) = (min

x j ∈S Div ij1 , ..., min x j ∈S Div ijl ) (8.8)
h S (x i ) = (avg x j ∈S Div ij1 , ..., avg x j ∈S Div ijl ) (8.9)

h S (x i ) = (max x j ∈S Div ij1 , ..., max x j ∈S Div ijl ) (8.10)
where Div ijk , k ∈ {1, ..., l} are diversity feature vectors incorporating semantic diversity information. These various pairwise semantic diversities include pairwise euclidean distance based subtopic diversity given latent subtopic vectors learnt from Probabilistic Latent Semantic Analysis (PLSA), formulated as,

Div topic ij = m k=1 (p(z k |x i ) -p(z k |x j )) 2 (8.11)
where z k , k ∈ {1, .., m} are the latent topics learnt from PLSA, and x i and x j are different documents. They also include pairwise cosine dissimilarity text diversity based on weighted term vector representations (TF-IDF), formulated as,

Div text ij = 1 - d i • d j ∥d i ∥∥d j ∥ (8.12)
where d i and d j are the TF-IDF document vectors for documents x i and x j . However, [START_REF] Qin | Promoting diversity in recommendation by entropy regularizer[END_REF] points out semantic information may be incomplete and thus unreliable, leading to exploit latent item vectors learnt from explicit features (ratings etc.) or implicit features (clicking, viewing etc.) to measure diversity of the returned list. It is argued that latent vectors learnt from these features reflect the underlying features of items thus the more orthogonal two latent vectors are the more dissimilar they are.

Diversification

Traditional IR/recommendation tasks have concentrated on estimating a precise relevance or affinity of the documents and candidate items, who will cause redundancy and dissatisfaction of the rendered results. Thus, it is essentially to apply diversification in IR/recommendation tasks for a both accurate and diverse result. As we have discussed in previous section (8.1), diversity does not have a universal definition and thus various diversification methods may be possible according to a specific setting of diversity. Corresponding to various diversities in information retrieval problems, various diversification methods [START_REF] Carbonell | The use of mmr, diversity-based reranking for reordering documents and producing summaries[END_REF][START_REF] Borodin | Max-sum diversification, monotone submodular functions, and dynamic updates[END_REF][START_REF] Rodrygo | Exploiting query reformulations for web search result diversification[END_REF][START_REF] Qin | Promoting diversity in recommendation by entropy regularizer[END_REF] have been proposed. In this section, we first present query reformulation based diversification whose main idea is to unravel user's different intents for diversified results. Then we introduce post-processing re-ranking methods which consider an optimization of linearly combined accuracy and diversity function for achieving both accuracy and diversity. Finally we present diversification models which in models themselves have combined accuracy and diversity in an intelligent way.

Query Disambiguation for Diversification

In information search scenarios, search result diversification targets query disambiguation, leading to query reformulation methods for diversification [START_REF] Rodrygo | Exploiting query reformulations for web search result diversification[END_REF], and intent-based [START_REF] Rakesh Agrawal | Diversifying search results[END_REF][START_REF] Rodrygo | Intent-aware search result diversification[END_REF][START_REF] Hu | Search result diversification based on hierarchical intents[END_REF] diversification. Query reformulation is a process to generate representations of query aspects in the form of sub-queries [START_REF] Rodrygo | Exploiting query reformulations for web search result diversification[END_REF], and there exist different techniques for this process. The term aspect refers to different interpretations of ambiguous queries, which can be extracted from each query. The term intent refers to the type of a query / the purpose of a user, informational or navigational for example. xQuAD [START_REF] Rodrygo | Exploiting query reformulations for web search result diversification[END_REF] defines for a candidate document d the diversity score shown in Eq. (8.6). The original query q is reformulated into Q = {q i |i ∈ |Q|}. The xQuAD framework returns a diversified document list by iteratively selecting from the candidate documents a document which can maximize the mixture of relevance and diversity estimation. However, in case of recommendation, intent or aspect of each user are not explicitly available.

Post-processing Re-ranking for Diversification

Different post-processing diversification techniques [START_REF] Carbonell | The use of mmr, diversity-based reranking for reordering documents and producing summaries[END_REF][START_REF] Borodin | Max-sum diversification, monotone submodular functions, and dynamic updates[END_REF][START_REF] Qin | Promoting diversity in recommendation by entropy regularizer[END_REF] have been proposed in information retrieval tasks to re-rank the documents. MMR (Maximal Marginal Relevance) [START_REF] Carbonell | The use of mmr, diversity-based reranking for reordering documents and producing summaries[END_REF] defines a marginal relevance that linearly combines the relevance and accumulated dissimilarity, and maximizes this marginal relevance to diversify the ranking by taking the form,

ω * i = arg max ω i ⊆X\S [λSim 1 (ω u , ω i ) -(1 -λ)max ω j ∈S Sim 2 (ω i , ω j )] (8.13)
where S is the subset of already selected items, λ is the parameter to adjust the trade-off between relevance and diversity. Sim 1 measures the relevance between the item and the user and Sim 2 measures the similarity between two items. And λ adjusts the proportion of relevance and accumulated dissimilarity, giving a standard recommendation list when λ = 1 and a purely diversified list when λ = 0.

Maxsum [START_REF] Borodin | Max-sum diversification, monotone submodular functions, and dynamic updates[END_REF] describes the diversification problem as to optimize the linear combination of a submodular quality function f (S) over the result list S and the max-sum dispersion Entropy [START_REF] Qin | Promoting diversity in recommendation by entropy regularizer[END_REF] takes probabilistic matrix factorization (PMF) method as base algorithm and assumes user latent vectors and item latent vectors both have the Gaussian distributions. And they propose to takes a linear form combining the quality measuring of the recommendation list and diversity promoting regularizer defined by different entropy of the assumed distribution of ratings, noted as,

arg max S:|S|<K f (S) ≡ R(S) + λg(S) (8.15)
where R(S) and g(S) are separately represented as,

R(S) ≡ ω∈S (E[r ω | r Ω , V ] -c) (8.16) g(S) = h(r S | r Ω , V ) = 1 2 | S | log(2πe) + 1 2 logdet(Σ S ) (8.17)
where Ω the set of rated items of the user and S the unrated items, r ω predicted rating of the item, Σ the covariance matrix of items, V the item feature matrix and c a constant. The proposed differential entropy g(S) is submodular and will be maximized when item latent vectors are orthogonal to each other (if that is possible).

Diversification Models

[83] presumes the existence of a taxonomy information with both queries and documents categorized using this information. They denote the set of categories belonging to a query q as C(q) and that belonging to a document d as C(d). Besides they also presume knowing the distribution of a given query belonging to a given category, denoted as P (c|q) and the likelihood of a document d satisfying the intent c for the query q as V (d|q, c). Based on these presumptions they define the top-N diversification problem in a probabilistic form over a set of documents D for a query q as such,

P (S|q) = c P (c|q)(1 - d∈S (1 -V (d|q, c))) (8.18)
where S is the topN diversified result and |S| = N .

Recently, determinantal point processes [START_REF] Kulesza | Structured determinantal point processes[END_REF] (DPPs) have been widely applied to various diversification tasks in machine learning. DPPs are equipped with a positive semi-definite kernel matrix L. Following Kuelsza et al. [START_REF] Kulesza | Structured determinantal point processes[END_REF], this kernel matrix can be decomposed as Gram matrix, with each entry denoted as L ij = q i ϕ ⊤ i ϕ j q j , where q i and q j measure the quality of item i and j and ϕ i and ϕ j are normalized feature vectors to help measure the similarity of items by applying ϕ ⊤ i ϕ j . However, in personalized recommendation settings, the quality of items varies from one user to the other and thus the normalized feature vectors of items may not directly be deduced from CF results.

PDGAN [START_REF] Wu | Pdgan: Adversarial learning for personalized diversity-promoting recommendation[END_REF] is a method that combines the diversification model DPP with generative adversarial network (GAN). However the base model for the discriminator and generator model in GAN framework is based on a matrix factorization methods (PMF [START_REF] Salakhutdinov | Probabilistic matrix factorization[END_REF]) which only considers the user-item interactions, therefore the performance of PDGAN does not benefit from auxiliary information for better accuracy.

Part III Knowledge Graph Embedding

Introduction

Recommender systems (RS) have been intensively studied over the last three decades and have reached a remarkable effectiveness. Amazon, Netflix, Facebook: all these applications and e-commerce sites make a very intensive use of recommender systems. Top-N recommender systems, as one of main recommendation applications, exploiting user-item interactions have achieved amazing recommendation results.

Top-N recommendation aims at selecting a set of N items that represents the highest relevance to a user. Among various kinds of recommendation techniques, collaborative filtering methods (CF), in particular model-based matrix factorization methods such as [START_REF] Salakhutdinov | Probabilistic matrix factorization[END_REF][START_REF] He | Fast matrix factorization for online recommendation with implicit feedback[END_REF], have been widely suggested due to their predictive power in terms of accuracy. They make use of user-item interactions in order to determine item relevance towards users, which in general generate rather accurate predictions.

However, the use of only one type of relations (user-item interaction) lacks explicit semantics and implies the search for latent user-item relations. Besides, apart from useritem interactions (among which rating is commonly used), there exist various relations between items and other entities that could be helpful for a better understanding of the users' behaviour. All these relationships can be modeled as a graph structure that provides richer information about the users, items, and their interactions. Mind that this graph may also contain the direct user-item interaction as one of its relations and therefore, can be seen as an extension of CF model. Furthermore, knowledge graph embedding methods [START_REF] Bordes | Translating embeddings for modeling multi-relational data[END_REF][START_REF] Wang | Knowledge graph embedding by translating on hyperplanes[END_REF][START_REF] Ji | Knowledge graph embedding via dynamic mapping matrix[END_REF][START_REF] Lin | Learning entity and relation embeddings for knowledge graph completion[END_REF], naturally capturing and conserving different types of relations among various kinds of entities including users, items and others, can provide a promising model for this purpose. F. Zhang et al. propose the framework CKE [START_REF] Zhang | Collaborative knowledge base embedding for recommender systems[END_REF] incorporating one translation-based embedding method Bayesian TransR for recommendation. X. Xin et al. [START_REF] Xin | Relational collaborative filtering: Modeling multiple item relations for recommendation[END_REF] propose a two-layer relational collaborative filtering method RCF to exploit knowledge graph embedding for top-N recommendation. Both of them have revealed improved performance of recommendation accuracy due to exploiting structural information on knowledge graphs. However, accuracy should not be the ultimate goal of the recommendation task as it results in returning to the user highly similar items, ignoring the relations between them, and finally, decreasing user's satisfaction with the provided service. For example, in E-commerce, after detecting a user's interest in laptops, a recommender system returning a list purely composed of laptops is inefficient as the user is very unlikely to purchase more than one model at a time. In movie recommendation, users may get bored after watching several theme-alike movies sequentially. Thus, a returned list of items should be diverse enough, implying both, redundancy reduction and novelty increase.

Despite the importance of diversity, it has received much less attention than accuracy in top-N recommendation domain. Carbonell and Goldstein provide a diversification method Maximal Marginal Relevance (MMR) [START_REF] Carbonell | The use of mmr, diversity-based reranking for reordering documents and producing summaries[END_REF] for re-ordering the items through an iterative process by selecting the most dissimilar item to the existent item list. Further, A. Borodin et al. [START_REF] Borodin | Max-sum diversification, monotone submodular functions, and dynamic updates[END_REF] provide its extended version and redefine the problem as max sum diversification problem in order to give a theoretically provable solution. However, these diversification solutions adopt pairwise similarity which tends to be sub-optimal as it ignores the correlation within the item list.

A recent emergence of determinantal point processes (DPPs) brings new potential to enhancing diversity in multiple machine learning problems, such as extractive summarization [START_REF] Kulesza | Learning determinantal point processes[END_REF] and basket completion [START_REF] Gartrell | Bayesian low-rank determinantal point processes[END_REF][START_REF] Warlop | Tensorized determinantal point processes for recommendation[END_REF]. DPPs are probabilistic models of sets parameterized with positive semi-definite matrix which characterizes naturally both element-wise relevance towards a query/user and the repulsiveness of subsets on the total candidate item set. DPP captures item similarity in an unified feature space and propose list-wise dissimilar items. Thus, using DPP in recommendation models improves their results in terms of diversity. The challenge here is to find an efficient way to construct the positive semi-definite kernel matrix in order to balance relevance and diversity of items.

Though, a bunch of work have been done recently to address the problem of diversity in recommendation (e.g. [START_REF] Carbonell | The use of mmr, diversity-based reranking for reordering documents and producing summaries[END_REF][START_REF] Vargas | Coverage, redundancy and size-awareness in genre diversity for recommender systems[END_REF][START_REF] Rodrygo | Exploiting query reformulations for web search result diversification[END_REF][START_REF] Rodrygo | Intent-aware search result diversification[END_REF][START_REF] Wu | Pdgan: Adversarial learning for personalized diversity-promoting recommendation[END_REF][START_REF] Tulio Ribeiro | Paretoefficient hybridization for multi-objective recommender systems[END_REF][START_REF] Chen | Fast greedy map inference for determinantal point process to improve recommendation diversity[END_REF][START_REF] Gan | Enhancing recommendation diversity using determinantal point processes on knowledge graphs[END_REF]), achieving a good accuracy-diversity trade-off is still an open challenge. Thus, most of existing works confront with this trade-off assuming submodular feature of optimisation function. A few works [START_REF] Wu | Pdgan: Adversarial learning for personalized diversity-promoting recommendation[END_REF][START_REF] Sun | A framework for recommending accurate and diverse items using bayesian graph convolutional neural networks[END_REF][START_REF] Cheng | Learning to Recommend Accurate and Diverse Items[END_REF] try to find solutions both diverse and accurate. However, there is still a lack of the understanding of a good trade-off between accuracy and diversity and when and how a better trade-off can be achieved. In our opinion, a diversity-aware recommendation algorithm should not only achieve both high accuracy and diversity, but also be robust under different parameter settings.

To address the accuracy-diversity trade-off problem, we propose two models: DivKG and EMDKG respectively in Chapter 11 and Chapter 12. DivKG is, to our best knowledge, the first method that combines knowledge graph embedding with determinantal point processes for a diversified recommendation. The combination of the two approaches KGE and DPP, we propose a new approach to construct the personalized DPP kernel matrix based on KGE results. EMDKG is another approach for diversified recommendation, which jointly optimizes an item diversity learning and knowledge graph embedding for obtaining better representations to capture semantic diversity.

The roadmap of the rest of this part is described as such. We first introduce the background of our proposals in Chapter 10. Then in Chapter 11 and Chapter 12 we respectively detail our two diversified recommendation models DivKG and EMDKG. And finally in Chapter 13 we conlude this part.

Background

The goal of our recommendation task is two-fold: given a set of users U , a set of items I, the user-item interactions R 0 , item-side auxiliary information R i , i ∈ {1, 2, ...} the top-N recommendation should provide each user u ∈ U with relevant yet diverse recommendations. As we have presented in Part II, diversity metrics play a fundamental part in defining our problem since the definition of the diversity itself usually lies on a diversity metric. Moreover, both our solutions DivKG and EMDKG lie on two ideas: Determinantal Point Processes and Translation-Based Knowledge Graph Embedding. Thus, to better introduce our models, first we present briefly these three parts in this section to provide the background.

Diversity Metrics for Recommendation

A diverse top-N recommendation means providing each user with a diverse list of N items, which requires a measurement of how diverse a given item list is. Two points are worthy noticing for the choice of this measurement: (1) in the state-of-the-art recommendation algorithms [START_REF] Xin | Relational collaborative filtering: Modeling multiple item relations for recommendation[END_REF][START_REF] Salakhutdinov | Probabilistic matrix factorization[END_REF][START_REF] Rendle | Bpr: Bayesian personalized ranking from implicit feedback[END_REF][START_REF] Kabbur | Fism: Factored item similarity models for top-n recommender systems[END_REF][START_REF] Wang | Irgan: A minimax game for unifying generative and discriminative information retrieval models[END_REF], users and items are usually represented in continuous vector space or embedded space; thus the measurement of a item list should be more convenient to be operated on latent vectors in practice. [START_REF] Chen | A music recommendation system based on music data grouping and user interests[END_REF] for users and more generally human beings, diversity of an item list is easier to understand when it is equipped with human understandable features or semantic information, namely categories, topics, co-activities etc. So it makes more senses to utilise the semantic information for providing diverse solutions.

Regarding the first point, as items are represented as latent vectors, it is necessary to define diversity measurement Div(•) : R N → R for a list of vectors V = {v 1 , ..., v N }. Different metrics for this have been proposed in existing works. One type of diversity measures for a list of vectors is inspired by pairwise vector diversity (dissimilarity). The definitions of pairwise similarity and pairwise diversity are then given as follows.

Definition 2. (Pairwise Similarity)

A pairwise similarity Sim pair is a real-valued function defining the similarity of two vectors. And it is usually related to the inverse of distance in vectorial space.

Definition 3. (Pairwise Diversity)

A pairwise diversity is a real-valued function defining the diversity of two vectors. When measuring on a list of two items, the diversity equals to the dissimilarity or the inverse of pairwise similarity or distance in vectorial space.

More particularly, common pairwise similarity metrics include inner product and cosine similarity. And we formalize the two similarity metrics given two vectors v i and v j as such:

inner_product : ⟨v i , v j ⟩ = v ⊤ i • v j = k d=1 v d i * v d j (10.1) cosine_similarity : cosine(v i , v j ) = ⟨v i , v j ⟩ ∥v i ∥ * ∥v j ∥ (10.2)
As the pairwise diversity is the inverse pairwise similarity, it is apparent to choose -Sim pair for the convenience. Based on pairwise diversity, we can define diversity metric for a list of item vectors, named as pairwise based Intra-List Diversity (ILD), formulated as, ILD :

i∈L j∈L&j̸ =i -Sim pair (v i , v j ) (10.3)
where L is the list of items.

Another category of vector diversity is directly listwise and based on the determinant of square matrix V ⊤ V , where V = [v 1 , ...nv L ] is the vector of item vectors.

Div det : det(V ⊤ V ) = det           v 1 • v 1 ... v 1 • v L ... ... v L • v 1 ... v L • v L           = def           ∥v 1 ∥ 2 ... sim(v 1 , v L ) ... ... sim(v L , v 1 ) ... ∥v L ∥ 2           (10.4)
The form of determinant of the item representation square matrix corresponds to a rather complicated relation in terms of vector pairwise similarity. And such a form actually can consider more than pairwise dissimilarity but also multi-item diversity [START_REF] Kuo | Emotion-based music recommendation by association discovery from film music[END_REF][START_REF] Bomhardt | Newsrec, a svm-driven personal recommendation system for news websites[END_REF], up to L -1).

On the other hand, to render diversity measurement more human comprehensible, diversity metrics relying on semantic information can be defined. The semantic information of items can be explicitly categories of items, labels or tags given to the items or implicitly a co-activity of two items [START_REF] Abbassi | Getting recommender systems to think outside the box[END_REF]. Take movies as an example, genres or textual tags of movies are explicit features, while movies co-played or co-liked are implicit characteristics to evaluate the similar the movies. It is admittedly more straightforward, however, to consider the explicit features as rule of thumb for item semantic diversity. Thus we formalize the explicit features here. To be noted, different terms have been designated to refer item features, i.e. topics and categories, here we use these terms interchangeably. Definition 4. (Item feature) An item feature f is an explicit description unit for an item i.

Two different item features may have correlations or not, but we can calculate the diversity based on item features (or semantic diversity) of an item list given each item's item feature information. And the semantic diversity is both motivation and evaluation criteria to achieve diversified recommendation. Definition 5. (Item feature set) Given a ground feature set F = {f 1 , f 2 , ..., f M } where the count of features is M , an item feature set is a subset of F for item i, denoted as

F i ⊆ F , meaning the item i possessing each feature f ∈ F i .

Definition 6. (Semantic diversity)

A semantic diversity is a quantitive measure over a set of N items I = {i 1 , i 2 , ..., i N } equipped with item features F = {F i |i ∈ I}, denoted as div(•). F i is the i-th item's feature set. Definition 6 gives a general concept and denotation but specific formulations of how to use item feature sets to calculate a given item list should be defined. Definition 7 is a list-wise measure of semantic diversity, calculating the percentage of categories covered by an item list. Category Coverage as a diversity metric, however, only consider the presence of the features, but does not consider the repetitiveness or the position of the item in the list. Thus diversity metrics such as α-NDCG and DNG are brought to discount the repeating categories. α-NDCG@n [START_REF] Charles | Novelty and diversity in information retrieval evaluation[END_REF] is formulated as,

α-NDCG@n = 1 |U | |U | u=1 αDCG u @n αIDCG u @n (10.6)
in which

αDCG u @n = n k=1 L l=1 J u kl (1 -α) q u l,k-1 log 2 (1 + k) (10.7)
where J u kl equals to the rating of the kth item in the list for user u if kth item belongs to the genre l otherwise 0. q u l,k-1 counts the number of items belonging to genre l up to the k -1 position in the list, which accompanying the constant α to modify the redundancy in the recommendation list. αIDCG u @n denotes the largest value of αDCG u @n which achieves the ideal diversification of recommendation lists.

And DNG [START_REF] Shi | Adaptive diversification of recommendation results via latent factor portfolio[END_REF] also takes a discounted factor for categories and is formulated as,

DNG@N = N k=1 w k G(k) (10.8)
where w k is a discount factor taking w k = 1/2 k-1 and G(k) denotes the number of categories of the kth item has while the first k -1 items don't.

Another category of diversity Intra-List Diversity measures base on pair-wise distance of any two items in the item list. Here Intra-List Diversity resembles tremendeously to the PB-ILD for vector diversity, but here distance function inside ILD is a function defined on binary representations, instead of real-values vectors.

Determinantal Point Processes

A determinantal point process (DPP) is a probabilistic model over selection of points.

Originating from quantum physics, this model is characterized by its repulsiveness, which means a higher probability of a subset selection associates with more repelling points to each other in the subset [START_REF] Kulesza | Learning determinantal point processes[END_REF]. DPP P over a discrete point set Ω = {ω 1 , ω 2 , .., ω M } is determined by a M × M positive semi-definite matrix L indexed by the elements from Ω and defining the probability of point selection. In our case, Ω is the set of items.

Given a discrete point set Ω, a determinantal point process P is a probability measure defined on 2 Ω , the set of all subsets of Ω, such that if A ∼ P is a random subset, then we get:

P(A = A) ∝ det(L A ) (10.10)
where

L A ≡ [L ij ] ω i ,ω j ∈A .
The diagonal elements of L provide the probabilities of selecting individual items from Ω (P(ω i ) ∈ W, i = 1, ...M ), while the off-diagonal elements of L reflect the negative correlations between item pairs. The larger the values of L ij , the smaller the tendency of ω i and ω j to co-occur. The determinants of entries L ij can be viewed as measurements of the similarity between ω i and ω j . Therefore, more similar items are less likely to get selected together. In the RS context , the diagonal elements L ii can be seen as user's affinities towards an item ω i .

When given the kernel matrix L for the determinantal processes, we can apply DPP sampling methods [START_REF] Chen | Fast greedy map inference for determinantal point process to improve recommendation diversity[END_REF][START_REF] Gillenwater | A treebased method for fast repeated sampling of determinantal point processes[END_REF] based on kernel matrix to retrieve diversified top-N recommendation list. Thus, in RS context,the main task of using DPP for diversified recommendation goes to the construction or the learning of the personalized kernel matrix.

For the learning of kernel matrix, we consider a pairwise loss function between selected and all remaining items, and uniform sampling under the framework of Bayesian Personalized Ranking (BPR) [START_REF] Rendle | Bpr: Bayesian personalized ranking from implicit feedback[END_REF]. For instance, given a user u ∈ U , the set of items I, the BPR loss function for the parameter vector of an arbitrary model class Θ is defined as:

L BP R = (u,i,j)∈D T ln σ(x uij ) -λ Θ ||Θ|| 2 (10.11)
where σ(x) = 1 1+e -x is the logistic sigmoid function, xuij (Θ) is a model specific function estimating a real value of preferences of user u and items i and j, λ Θ are model specific regulation parameters, D T : U × I × I, s.t.

D S = (u, i, j)|i ∈ I + u ∧ j ∈ I \ I + u (10.12)
, and (u, i, j) ∈ D S denotes that the user u prefers the item i over j, T ⊆ U × I being the available user-item interactions and I + u = {i ∈ I : (u, i) ∈ T }. The estimator xuij is decomposed as xuij = xuixuj . We will specify the function used for optimisation in Section 12.3.

Translation-Based Knowledge Graph Embedding for

Recommendation

A knowledge graph (KG) is a multi-relational graph (V, Edges, R) consisting of nodes v ∈ V , i.e. entities such as users, items, genres, actors, etc., and edges e ∈ E defining a relation between them r ∈ R (e.g. user-item interaction, belonging to a category, being directed by a certain person, etc.). Thus, an edge e ∈ Edges is a triplet of the head (or left) entity h ∈ V , the relation r ∈ R, and the tail (or right) entity t ∈ V , i.e. e = (h, r, t). We denote by r 0 the affinity relation between a user and an item (user-item interaction), and by r j any other relation between entities.

The main idea of translation-based embedding is to project the entities and the relations of the knowledge graph into the embedding space, i.e. a d-dimensional vector space R d . Thus, to each entity ,t) is defined to measure the plausibility that the triplet is incorrect. In other words, the relation should correspond to a translation of the embedding. Various score functions have been proposed for achieving better accuracy for tasks as link prediction, node classification and recommendation [START_REF] He | Translation-based recommendation[END_REF]. Here we use two forms of score functions from TransE and TransH as examples of KGE for recommendation. More advanced and complex forms of score functions are believed to provide a better performance. The score function of TransE [START_REF] Bordes | Translating embeddings for modeling multi-relational data[END_REF] is given by:

h ∈ V (resp. t ∈ V ) corresponds a vector v h ∈ R d (resp. v t ∈ R d ). A score function f r (h
f E r (h, t) = ||v h + v r -v t || p , v r ∈ R d (10.13)
.

TransH [START_REF] Wang | Knowledge graph embedding by translating on hyperplanes[END_REF] projects the embeddings v h and v t to a relation-specific hyperplane w r and considers the relation-specific translation vector v r in w r . Its score function is defined as:

f H r (h, t) = (v h -w T r v h w r ) projection of v h to wr + d r -(v t -w T r v t w r ) projection of v t to wr 2 2 (10.14)
where w r , v r ∈ R d . For training, the following margin-based ranking loss function [START_REF] Wang | Knowledge graph embedding by translating on hyperplanes[END_REF] can be used:

L KGE = (h,r,t)∈∆ (h ′ ,r ′ ,t ′ )∈∆ ′ f r (h, t) + γ -f r ′ (h ′ , t ′ ) + (10.15)
where [x] + ≜ max(0, x), γ is the margin between positive and negative triplets, ∆ and ∆ ′ denote the sets of positive and negative triplets, respectively. The negative triplets (h ′ , r ′ , t ′ ) are the results of the corruption of (h, r, t).

Furthermore we give the definiton of Diversty-Aware Knowledge Graph Embedding, where the item representations should capture the semantic diversity. After obtaining the latent vectors of users, items, other entities and relations, personalized kernel matrix can be constructed for each user. Finally we render each user a diversified recommendation list of items by the fast greedy MAP inference algorithm on its corresponding kernel matrix.

M i ,M j of M, if div s (M i ) ≤ div s (M j ) then div v (v M i ) ≤ div v (v M j ).

Knowledge Graph Embedding for Entity and Relation

Representations

To improve the accuracy of recommendation, one can make use of additional information incorporated into collaborative filtering methods. Recently, using knowledge graphs to model this kind of data has been shown to enhance the recommendation [START_REF] Zhang | Collaborative knowledge base embedding for recommender systems[END_REF][START_REF] Xin | Relational collaborative filtering: Modeling multiple item relations for recommendation[END_REF].

In this paper, we argue that knowledge graph is a robust and meaningful model that helps to blend multiple relations in one data structure. However, different from [START_REF] Xin | Relational collaborative filtering: Modeling multiple item relations for recommendation[END_REF], where solely items are taken as vertices of the knowledge graph, we propose to consider all entities engaged in the recommender system, including users, items and other additional entities (e.g. genre, actor, etc.). Moreover, we consider user-item interaction used traditionally for CF-based methods just as a specific type of relation on the knowledge graph. More formally, we represent every relation instance as a triplet (h, r, t) having semantic interpretation, where h and t denote the head and tail entities linked by one relation r.

Representation Learning for Entities and Relations

To apply embedding on such a knowledge graph, we represent each entity and each relation as a vector, i.e. h, r, t are represented as v h , v r ,v t , respectively. We use translation-based embedding methods [START_REF] Bordes | Translating embeddings for modeling multi-relational data[END_REF][START_REF] Wang | Knowledge graph embedding by translating on hyperplanes[END_REF] to interpret the translation semantics among vectors v h , v r , v t which is translation(v h , v r ) ≈ v t . We use a margin-based loss function with margin γ to optimise the vector representation:

Loss KGE = (h,r,t) (h ′ ,r ′ ,t ′ ) [f r (h, t) + γ -f r ′ (h ′ , t ′ )] + (11.1)
The corrupted triplets (h ′ , r ′ , t ′ ) are derived from golden triplets (h, r, t) by ( 1) keeping the relation unvaried, i.e. r = r ′ , and (2) by either keeping unvaried the head entity and randomly selecting the tail entity, i.e. h ′ = h, t ′ ̸ = t, or keeping unvaried the tail entity and randomly selecting the head entity, i.e. t ′ = t, h ̸ = h ′ . And f r denotes the translation function: TransE [START_REF] Bordes | Translating embeddings for modeling multi-relational data[END_REF] takes

f r (h, t) = ∥v h + v r -v t ∥ 2 (11.2)
TransH [START_REF] Wang | Knowledge graph embedding by translating on hyperplanes[END_REF] takes

f r (h, t) = ∥(v h -w r ⊤ v h w r ) + v r -(v t -w r ⊤ v t w r )∥ 2 (11.3)
where w r is a projection vector.

Top-N Prediction Based on Knowledge Graph Embedding

We obtain the vectors of all entities and relations through the optimization of the loss function 11.1. And based on these vectors, we can first generate a non-diversified top-N recommendation list for each user by measuring the similarity of users and items using the translation function (quality function). We notice that the translation function denotes the distance between two entities related by a relation and the further away two entities are the less similar these two entities are. Thus, to generate the topN item list for each user, we select N items with lowest translation values as the top-N recommendation result. Here, we propose to exploit determinantal point processes (DPP) models to improve feature representation-based diversity, where feature representations are generated on the previous step, i.e. knowledge graph embedding (KGE). Note, that our framework is modular, and allows other quality estimation techniques to be used as input to the current step. However, we argue that the combination of KGE and DPP is the most efficient in terms of diversity-accuracy trade-off.

Diversity-Aware Recommendation on Determinantal Point

Construction of DPP Kernel Matrix

DPPs are a group of probability models to reflect the distribution of items from item list X over the set Y, Y ⊆ 2 X , where the selection of a subset S, S ∈ Y of items is proportionate to the indexed determinant of the kernel matrix of DPP [START_REF] Kulesza | k-dpps: Fixed-size determinantal point processes[END_REF]. The kernel matrix of DPP is a positive semi-definite matrix which records the inherent affinity of each item appeared in the set Y and the similarities of every pair of two different items. More specifically the diagonal elements of the kernel matrix reflect the inherent affinity of each item and the non-diagonal elements reflect the pairwise similarity of the item set.

In order to construct a kernel matrix L u for each user u for top-N diversified recommendation, we define two auxiliary matrices. The first is user's u affinity profile w.r.t. candidate items defined as a diagonal matrix A u = diag(a 1 , ..., a m ), where m is the number of candidate items,

a i = e -(fr(u,i)-δ)
j∈X,j̸ =i e -(fr(u,j)-δ) (11.4) where f r (u, i) is the result of the item quality estimation function calculated in the previous step and δ is the average of f r (u, i) for u. We consider here the embedding translation function for user u, item i and translation type r. Here, we use the sof tmin function to normalize the affinities of all items for each user as the item quality function f r (u, i) from the knowledge graph embedding measures the distance of a pair of user u and item i by the relation r. And the more similar between u and i the smaller the distance value is. The second matrix reflects item pairwise and listwise similarity and is defined as

D u = [d ij ] m×m , whose entries d ij = e -fr 0 (i,j)
k∈X,k̸ =i e -fr 0 (i,k) (

and d ii = 0, where f r 0 (i, j) is the result of the embeddings of items i and j and relation r 0 , whose vector v r 0 = -→ 0 if items i and j share the same relation value (category). Finally, the kernel matrix L u for user u can be defined as:

L u = αA u + D u (11.6)
where α is a parameter to adjust the trade-off between user's affinities and similarities among the items, or in other words, between accuracy and diversity. In table 11.1 we demonstrate a visualized kernel matrix under our construction approach.

MAP Inference for Diversified Prediction

After the construction of the kernel matrix for each user u, we aim at selecting a list S of size N of items from total candidate items, s.t.

S map = argmax S∈Y,|S|=N logdet(L S ) (11.7) item 1 item 2 item 3 ... item M item 1 a u1 ... item 2 a u2 ... item 3 a u3 ... d 3M ... ... item M ... a uM
Table 11.1: The construction of personalized kernel matrix for DPP. For a user having M candidate items, we construct a M × M dimension matrix where the diagonal element representing the affinities of each item towards the user (a u1 for example represents the affinity or relevance for item 1 towards user u) ;and non-diagonal element representing the pairwise similarity of items (d 3M for example represents the similarity between item 3 and item M ). Due to the properties of DPP, such a kernel matrix will garantee a set of items with high affinity and diversity will be more likely to be selected from all candidate items.

where L S is the kernel matrix L u indexed by items from S. We recall that the probability of selecting a subset S is proportionate to the determinant of the indexed kernel matrix and DPP promotes a diversified selection of items under its property by definition. Thus, the selected items with the maximum log determinant value theoretically determine the best related and diverse top-N items for user u. However, such an optimization problem has been proven to be NP-hard, thus we use the fast greedy algorithm proposed by [START_REF] Chen | Fast greedy map inference for determinantal point process to improve recommendation diversity[END_REF] to retrieve an approximate top-N list as the diversified recommendation result. We refer to this DPP model with MAP inference as FastDPP. In Figure 11.3 we demonstrates the iterative procedure of how FastDPP selects items to return the top-N diverse items. 12 EMDKG: Diversity-Aware Representation Learning for a Better Trade-off Diversified Recommendation

In this chapter, we describe our second diversified recommendation framework EMDKG which targets at optimizing both item diversity representations and knowledge graph embedding for top-N recommendations. Our previous model DivKG proposes a quite elegant approach to conbine knowledge graph embedding with determinantal point processes for a diversified recommendation. However, the key part of contructing personalized DPP kernel matrix relies on an important assumption that item representation can fully capture the similarity/disimilarity among them. But the assumption may not be true all the time. An example is given as such. The motivation of this framework is that the representations of items should reflect the semantic diversity of items given a specific semantic diversity definition. And we can only do this by explicitly encoding this semantic information into item vectors. In the following of this paper, EMDKG E (resp. EMDKG H ) denotes our solution EMDKG incorporating Trans E (resp. Trans H ) knowledge-graph embedding.

General Overview

We propose an EM-schemed representation learning for recommendation. Corresponding to the two objectives for diversity-aware translation-based recommendation, the E-step aims at optimising translation-based knowledge graph representations for users, items and entities with a modified margin-based ranking loss for taking into account the diversity of item vectors. And the M-step aims at learning a diversity-encoded item representations with a pairwise BPR-based loss. The general model alternates the learning processes of these two parts until it converges. We demonstrate the framework EMDKG in Figure 12.1.

Diverse Item Sets Generation

As we want to encode semantic diversity information into item representation, it is important to possess ground-truth diverse item sets as benchmarks. That is to say, given a specific diversity metric and items with their semantic information, a set of diverse item sets should be given or generated using available information. As we are interested in top-N recommendation lists for each user, we also prefer to obtain diverse item sets with a fixed length. As it is not common that ground-truth diverse sets are provided in datasets, we propose a procedure to randomly generate fixed length diverse item sets. The procedure takes the historical user-item interactions and item categorical information, and generate ∆ random historically interacted item sets. Given a semantic diversity Div(•) we can calculate for each generated item set its semantic diversity score. Then we select sort the ∆ item sets by its diversity score in descending order and keep the highest as ground-truth diverse item sets. We note that ∆ should be sufficiently big for selecting diverse item sets. And we show this procedure in Algo. 1. Here, we denote the historical interacted items for each user u as I u candid and item categorical information as C I .

Algorithm 1 Diverse Item Set Generation

Inputs: U ,C I , N ,I candid , Div(•), ∆ Outputs: T 1: for u ∈ U do 2: RandomSet ← ∅ 3:
for ∆ times do 4:

Randomly generate a set T ′ of N items from I u candid 5:

Div(T ′ ) ← Calculate diversity score of the set T ′

6:

Append (T ′ , Div(C T ′ )) to RandomSet Diversity can be considered in terms of categories. In this case, one-hot encoding [START_REF] Zheng | Feature Engineering for Machine Learning: Principles and Techniques for Data Scientists[END_REF] can be used to represent item features. However, such approach becomes infeasible when the definition of diversity goes wider or the category number increases significantly. To overcome these limitations, vector representations can be used. Indeed, with the growing popularity of matrix factorisation and embedding techniques, modern RS largely rely on user and item representations in continuous vector space. We argue that diversity should be encoded in vector representations of items. To do so, we propose an item diversity learning framework with negative sampling.

We first need to demarcate the concepts of (a) semantic diversity based on the available information about the items (take categories/movie genres as example), and (b) vectorial diversity based on item vector representations and calculated using item vectors. In the Item Diversity Learning (IDL) module, we make use of both concepts. Our motivation behind that is as follows. In traditional RS, item vectors are often learnt by optimising item relevance to a given user profile (user vector). At the same time, a general principle is that similar users tend to like similar items. Thus, there exists a correlation between the similarity of items and their vector representations. However, it is not always the case.

A diversity measure div(•), whether on discrete or continuous space, should be defined to characterise the diversity for a given list. For instance, one can use pairwise vector dissimilarity metrics like intra-list average distance (ILAD) [START_REF] Zhang | Avoiding monotony: Improving the diversity of recommendation lists[END_REF], intra-list minimal distance (ILMD), or set-level metrics like category coverage (CC), α-NDCG and log-determinant of item-indexed kernel matrix employed in DPP [START_REF] Chen | Fast greedy map inference for determinantal point process to improve recommendation diversity[END_REF] defining diversity in the vector space of the entire list of items. As semantic information is handled in one-hot encoding on discrete space, only ILAD, ILMD, CC and α-NDCG can be used to calculate this information. In contrast, learned vector representations are in continuous vector space, and metrics as determinant, ILAD and ILMD are the possible diversity measures here.

For a given user u ∈ U , the IDL-module aims at learning the representations of items which can reflect the semantic diversity based on the available information (features, relations). As input, it takes the set of ground-truth item sets, denoted {T + }, each of the element T + (one individual item set) having the same size (length) consisting of the items the user had interactions with. We consider the item sets in this set to be the most diverse for each given user.

Based on each element from the ground-truth set T + and the remaining items I \ T + , the negative sampling is performed by randomly replacing all the items from T + except for one with the items from I \ T + .

Note that the size of the item sets is the same, i.e. |T -| = |T + |. The items for substitution are selected so that the overall semantic diversity of these negative item sets is inferior to the one of the ground-truth. In other words, if div(•) is a list diversity measure, then div(T + ) > div(T -) . At this step, we consider semantic diversity and suggest to apply dissimilarity measure on discrete space to calculate it. Thus, negative item sets T -are generated.

Once the negative items sets are constructed, the IDL-module learns item vector representations by optimising the following loss function:

L IDL = -log 1 + e -div(T + )+div(T -) .
Here, we make use of vectorial diversity and apply log-determinant measure to calculate it. Thus, the loss function gets the following form:

L IDL = A + ∈{T + } A -∈{T -} -log σ(log det(L A + ) -log det(L A -) (12.1)
where A + is the ground truth diverse item set, and A -is one item set from all negative item sets, L A + and L A -are the kernel matrix of DPP indexed with the elements from A + and A -, respectively. This kernel matrix is built as follows. Given an item list A ⊂ I, we notate with v A a vector representation of the item list A.

Then L A = v A v A
⊺ is a positive semidefinite matrix. The larger the value of the determinant det(L A ) is, the more diverse the item set A is [START_REF] Kulesza | Learning determinantal point processes[END_REF].

As the result of the IDL-module, we obtain vector representations of items that reckon with semantic similarity and vector similarity. And we demontrate the Item Diversity Learning module in Figure 12.2.

Modified Translation-Based Knowledge Graph Embedding for

Recommendation.

Auxiliary semantic information related to items such as categories, film directors, actors, etc. can provide valuable assets for enhancing recommendation accuracy [START_REF] Cao | Unifying knowledge graph learning and recommendation: Towards a better understanding of user preferences[END_REF][START_REF] Lee | News recommendation with topic-enriched knowledge graphs[END_REF]. Such auxiliary information can contain categorical information and relational knowledge with other entities which do not engage in the recommendation directly. It has been shown [START_REF] He | Translation-based recommendation[END_REF] that a translation-based knowledge graph embedding for recommendation can efficiently take into account (1) various entities that may affect user's preferences/choices for items and (2) different types of relations between them.

In this work, we take a similar approach to construct a knowledge graph as in DivKG, in terms of modelled relations, we distinguish between user-item interactions and any other relation between entities. We refer to the latter as auxiliary relations. Let r 0 be the relation between users and items reflecting a user-item interaction. As described in Chapter 7, for the triplet (u, r 0 , i) we can define a translation-based score function f r 0 (u, i) to measure the affinity value between the user u and the item i. The smaller the value of f r 0 (u, i) is, the larger the affinity between the user u and item i is. Similarly, we can define the score function f r j (i, e) for any auxiliary relation r j , j ∈ {1, 2, ...} between the item i and the auxiliary entity e ∈ E = V \ {U ∪ I}.

To learn the embedding accounting for both types of relations (user-item interactions r 0 and auxiliary relations r j,j̸ =0 ), we can rewrite the margin-based ranking loss function from eq. 10.15 as:

L KGE = (u,r 0 ,i) (u,r 0 ,i ′ ) [-f r 0 (u, i) + f r 0 (u, i ′ ), 0] + + (i,r j ,e) (i,r j ,e ′ )
[-f r j (i, e) + f r j (i, e ′ ), 0] + .

(12.2)

As stated above, such loss function aims at separating the golden triplets (both, historical user-item interactions and existent item-entity relations) from the negative triplets. However, conventional KGE only considers the existent relations of entities in the graph and does not explicitly optimize the diversity representations of item vectors as we do in Section ??. Thus we propose a modified knowledge graph embedding loss function to bridge KGE and Item Diversity Learning:

L xKGE = L KGE + KLDivergence V KGE I , V IDL I (12.3)
where V KGE I and V IDL I represent correspondingly the item vectors in KGE and Item Diversity Learning. We minimize KL-divergence of the vector representations of items in two modules in order to resemble the two item representations. Finally, we alternate the learning of knowledge graph embedding and item diversity learning by alternating optimisation of functions (eq. 12.1) and (eq. 12.3) until the the learning converges. Thus, we can formalize our proposal EMDKG as a dual-goal optimization problem of the Diversity-Aware Translation-Based Recommendation as follows.

(Diversity-Aware Translation-Based Recommendation.) Given a set of users U , items I, other entities E, historical user-item interactions H u,r 0 ,i and item-side relation information triplets H i,r j ,e , the diversity-aware translation-based recommendation aims at minimising two loss functions 12.1 and 12.3 simultaneously.

The process of co-learning is shown in Algorithm 2.

Algorithm 2 Co-learning of KGE and IDL

Inputs: T = {T + }, P = {(u, i)}, Q = {(i, r, e)}, k Outputs: V IDL I , V KGE I , V U , V R 1: Initialize V IDL I , V KGE I , V U , V R 2: while not converge do 3:
for k times do 4:

Get batch p ⊆ P and q ⊆ Q 5:

Optimize Eq.(12.3) with p and q 6: end for

7:

Get batch t ⊆ T

8:

Using negative sampling to obtain t -from t 9:

Optimize Eq.(12.1) with t and t - 10: end while

Prediction

To make a top-N recommendation, we take the learned vectors of users and items and affinity relation r 0 from KGE and calculate the affinity score for each user u with any item i using the score function f r 0 (u, i). For each user u ∈ U , we sort the items by ascending score function values, and return the top-N items as the result.

To further adjust the recommendation list, we can also apply diversification methods to balance the accuracy-diversity trade-off of the list. In diversification methods, such as MMR [START_REF] Carbonell | The use of mmr, diversity-based reranking for reordering documents and producing summaries[END_REF], XQuAD [START_REF] Rodrygo | Exploiting query reformulations for web search result diversification[END_REF], a threshold parameter that we denote α is used to adjust the trade-off between accuracy and diversity. For instance, MMR optimisation function is given by: max {αSim 1 (u, i) -(1 -α)max(Sim 2 (i, j))} (12.4) where Sim 1 (u, i) reflects the relevance of the item i to the user u, and Sim 2 (•, •) is a similarity measure between two items. We propose the following MMR-like determinant-based trade-off equation: The change of operations fromto + is due to the semantics of log det(•), interpreted as the dissimilarity of the item list •, contrary to the Sim 2 (•, •) being the similarity between any item pair. Q(u, i) is the affinity measure between any user-item pair (u, i). Higher value of Q(u, i) corresponds to closer affinity of the pair (u, i). However, in KGE setting, the lower the value of f r 0 (u, i) is, the higher the affinity is. Thus, we apply a monotonically decreasing function, i.e. e -x to satisfy the requirements of Q(u, i).

log det(L A ) ∝ α Q(u, i) + (1 -α) • log det(L A ) (12.

Conclusion

In

Conclusions

In the previous part we have presented two top-N diversified recommendation models DivKG and EMDKG based on knowledge graph embedding methods and determinantal point processes. To quantify the effectiveness of our proposals, in this part we will present their evaluations based on public real-world datasets for diversified top-N recommendation tasks. Before presenting the details of evaluation, I would like to recall that a diversified top-N recommendation task aims at achieving both high accuracy and diversity at the same time. Furthermore, as optimal accuracy and optimal diversity may not be able to be achieved at the same time, it is then required to discuss whether we can achieve a good trade-off between the two aspects. Finally, as both re-ranking diversification methods (e.x. MMR) and our methods select a diversified N item lists as recommendation results, we would also like to know how robust the models are in different settings.

To demonstrate all these, we first introduce in Chapter 15 the basic experimental settings including datasets information and common evaluation protocols applied in our experiments. Then we demonstrate separately in Section 16.1 and Section 16.2 the experiments on our models DivKG and EMDKG against state-of-the-art baselines in terms of accuracy and diversity metrics. We also give discussions along the experiments for each model.

Experimental Settings

Datasets

For the evaluation purpose, we construct our first multi-relation dataset by combining two real-world datasets (Movielens-100K and IMDb datasets). Our first dataset is MovieLens-100K (denoted ML-100K) containing 100,000 user ratings ranging from score 1 to 5 from 943 users on 1,682 movies. Each user has rated at least 20 movies. However, the rating matrix of ML-100K is still highly sparse, with a sparsity of 93.70%. The second dataset for the multi-relation dataset is IMDb Dataset which is currently released on IMDb website1 . It contains information including crews, principals, different releasing versions of more The anime genres are comedy, action, fantasy, sci-fi, drama, shounen, kids, romance, school, slice of life, hentai, supernatural, mecha, music, historical, magic, ecchi, shoujo, seinen, sports, mystery, super power, military, parody, space, horror, harem, demons, martial arts, dementia, psychological, police, game, samurai, vampire, thriller, cars, shounen ai, shoujo ai, josei, yuri, yaoi, and other. or more of the 44 non-exclusive genres available in the dataset, namely comedy, action, fantasy, sci-fi, drama, shounen, kids, romance, school, slice of life, hentai, supernatural, mecha, music, historical, magic, ecchi, shoujo, seinen, sports, mystery, super power, military, parody, space, horror, harem, demons, martial arts, dementia, psychological, police, game, samurai, vampire, thriller, cars, shounen ai, shoujo ai, josei, yuri, yaoi, and other. The statistics of Anime dataset for the genre information is shown in Figure 15.3 and the correlation between genre based on item-genre information is demonstrated in Figure 15.2(b). For processing of Anime datasets, we follow the same procedure as for ML100K-IMDb dataset and treat the rating data as implicit feedback and consider ratings of 6/10 and higher as positive feedback, resulting in more than 1.8 million of positive interactions.

As we employ the leave-one-out strategy, we randomly divide rating information contained in both ML100K-IMDb and Anime datasets into training/ validation/ testing datasets. The random division into training/validation/testing datasets are done in five times with different initial random seeds. The experiments are operated over five different divisions of each dataset and the average results are reported. Item-side auxiliary information are added to training datasets as relational information.

For EMDKG model, we need to generate ground-truth diverse item sets for a given user by following the procedure described in Section 12.2. We use items from historical user-item interactions as candidates and the given categorical information (genres) of items to randomly generate item sets of length 10 and keep the top-100 item sets with the highest semantic diversity scores.

All the experiments are written mostly in Python (PyTorch framework for model learning and prediction), and part of the re-usable libraries for knowledge graph embedding is written in C++, callable in Python. Experiments presented in this dissertation were carried out using the Grid'5000 testbed, supported by a scientific interest group hosted by Inria and including CNRS, RENATER and several Universities as well as other organizations (see https://www.grid5000.fr).

Evaluation Protocol

We evaluate our frameworks regarding the accuracy and diversity of the returned results. For both models the evaluation is performed in two steps. We first assess the quality of the embedding part, and then the results of diversification (DPP sampling) part.

For measuring accuracy of the top-N recommendation, we use two traditional metrics in information retrieval for document ranking:

1. Normalized Discounted Cumulative Gain (NDCG) [START_REF] Järvelin | IR evaluation methods for retrieving highly relevant documents[END_REF]: NDCG takes the positions (ranks) of correct items into consideration. Given a top-N recommendation list sorted in a descending order by a relative relevance, let rel u,j be the graded relevance of the recommendation at position j for the user u in the test set, and Z be the normalization constant. NDCG@N is then given by:

NDCG@N = 1 Z DCG@N = 1 Z N j=1
2 rel u,j -1 log 2 (j + 1) .

2. Hit ratio hit@N which only considers whether a test item is in the returned recommendation list and it is formulated as,

hit@N =      1 if ∃j ∈ N, rel u,j = 1 0 otherwise
We calculate both metrics hit@N and NDCG@N for each test user and report the average score.

To evaluate the performance of recommendation diversity, due to the differences of diversity definition in our models DivKG and EMDKG, we specify different diversity metrics for each method and the details of the diversity metrics are given in coming chapters for exhibiting experiments of each model.

For the two steps of evaluation, we apply the following evaluation procedure. To evaluate the accuracy performance of recommendation, we adopt the leave-one-out strategy which is widely used in literature [START_REF] Xin | Relational collaborative filtering: Modeling multiple item relations for recommendation[END_REF] in both knowledge graph embedding and DPP processes. Thus, for knowledge graph embedding part (see Section 11.1 and Section 12.4), for each user, we randomly select one user-item interaction (rating) to constitute our test set, and then we randomly split the remaining interactions to training set, and validation set with ratio 80 : 20, respectively. We add all the other auxiliary information triplets to the training sets for representation learning purpose.

For the diversification part using DPP (see Section 11.2) and Section 12.5 , we randomly hold one user-item rating and mix with a fixed length M most similar items calculated from knowledge graph embedding results. The length of M will be specified along with experiment results.

Experiment Results

In this chapter we demonstrate the experiments on our two proposals separately in Section 16.1 and Section 16.2.

Experiments on DivKG

Baselines

To compare the performance of the first step of our framework, we use the following baseline algorithms:

-BPRMF [START_REF] Rendle | Bpr: Bayesian personalized ranking from implicit feedback[END_REF]. This is a matrix factorization method optimised by a pairwise ranking loss (BPR-OPT, formulated in Eq. (6.22)) to learn from implicit feedback. This method only uses historical user-item interactions for learning and predicting recommendation and does not use relational data for learning process.

-FISM [START_REF] Kabbur | Fism: Factored item similarity models for top-n recommender systems[END_REF]. This is an item-based collaborative filtering method that considers a discount factor for the item and user latent vector multiplication. We also apply the pairwise ranking loss criterion BPR-OPT for the optimization of this method. We adopt and modify the implementation provided by [START_REF] Xin | Relational collaborative filtering: Modeling multiple item relations for recommendation[END_REF].

-RCF [START_REF] Xin | Relational collaborative filtering: Modeling multiple item relations for recommendation[END_REF]. This is a knowledge graph based method that considers both user-item interactions and other types of item relations and proposes a double-layer neural model for learning-to-rank top-N recommendation.

For the sake of a fair comparison, we combine the aforementioned models with two diversification models, namely our FastDPP (see Section 11.2.2) and the well-acknowledged diversification method MMR to compare recommendation performance both on accuracy and diversity. [START_REF] Carbonell | The use of mmr, diversity-based reranking for reordering documents and producing summaries[END_REF]. This is a re-ranking criterion to reduce redundancy while maintaining document relevance in the field of text summarization. Specifically, MMR iteratively chooses an item satisfying the following requirement:

Maximal Marginal Relevance (MMR)

ω * i = argmax ω i ⊆X\S [λr ω i -(1 -λ)max ω j ∈S sim(ω i , ω j )] (16.1)
where r ω i is the estimated rating of item ω i , S is the subset of already selected items, λ is the parameter to adjust the trade-off between relevance and diversity and sim(•) is the similarity function between two items. We notify that for when applying recommendation methods with MMR diversification, the sim(•) function is selected according to the recommendation method. More specifically, for BPRMF and RCF, we use cosine_similarity of item latent vectors to replace the sim(•) and for translation-based knowledge graph representations, we use translation function ∥h -t∥ (h and t to represent two item entities) to replace the sim(•) function.

Diversity Metrics

For DivKG, we assume the item latent vectors can capture the dissimilarity relation among each other well, i.e. the larger the similarity value of the item latent vectors the less diverse the corresponding items are. Therefore, to assess the diversity of the recommendation, we use two pairwise-based metrics defined on the item list used by [START_REF] Chen | Fast greedy map inference for determinantal point process to improve recommendation diversity[END_REF], where S ij denotes the similarity between i and j:

ILAD = mean u∈U mean i,j∈Ru,i̸ =j (1 -S i,j ) (16.2)
, and ILMD = mean

u∈U min i,j∈Ru,i̸ =j (1 -S i,j ) (16.3)
. We calculate ILAD and ILMD for each result list and report the average score.

Experimental Results

Recommendation Results for Applying Knowledge Graph Embedding Methods

To fairly compare the performance of different embedding methods, we train knowledge graph embedding by optimizing the margin loss with mini-batch Adam optimization [START_REF] Diederik | Adam: A method for stochastic optimization[END_REF].

The learning rate range is set as 0.001, 0.005, 0.01 and the batch size is set as 972 for ML-100K. The embedding size ranges from 50, 75, 100, 150. We have performed a grip search for finding the best results for each method. And in 16.1 shows a general accuracy improvement using translation-based knowledge graph embedding regarding user-item interactions as one kind of relations. The two translation-based embedding methods we use here, TransE and TransH, outperform not only classic BPR-based CF method (BPRMF) and item-based matrix factorization method (FISM), but also outperform the start-of-art relation collaborative filtering method RCF which also takes relation information into account for accuracy enhancement. We attribute this lower performance of RCF to both the separation of user-item interactions and other relations in the knowledge graphs and its fixed types of relations encoded on the knowledge graph. Moreover, TransH generally outperforms TransE due to the projection of entity vectors to a relation-specific hyperplane which enhances the accuracy.

Diversified Recommendation

Experiments on EMDKG 16.2.1 Baselines

We consider both diversified and not diversified baselines to evaluate EMDKG in terms of diversity, accuracy and diversity-accuracy trade-off:

-BPRMF [START_REF] Rendle | Bpr: Bayesian personalized ranking from implicit feedback[END_REF] is a matrix factorization approach that uses a pairwise ranking loss to provide recommendations. Similar to EMDKG, it considers implicit feedback. However, it does not focus on diversity, nor it uses relational information from knowledge graph. We have used it as a baseline for evaluating DivKG.

-FISM [START_REF] Kabbur | Fism: Factored item similarity models for top-n recommender systems[END_REF] is an item-based collaborative filtering method that considers a discount factor for the item and user latent vector multiplication. We also apply the pairwise ranking loss criterion BPR-OPT for the optimization of this method. We adopt and modify the implementation provided by [START_REF] Xin | Relational collaborative filtering: Modeling multiple item relations for recommendation[END_REF]. We have also used it as a baseline for evaluating DivKG.

-TransKG [.] ] [101] models users, items and all the associated entities in a knowledge graph, then uses the embedded vectors obtained with translation-based KG embedding, Trans E [START_REF] Bordes | Translating embeddings for modeling multi-relational data[END_REF] (TransKG E ) or Trans H [START_REF] Wang | Knowledge graph embedding by translating on hyperplanes[END_REF] (TransKG H ), to give the result. This actually corresponds to the knowledge graph embedding part in our previous model DivKG.

-IRGAN 1 [50] is a framework that makes compete a discriminative and a generative model in an adversarial way to solve several IR problems, including top-N recommendation.

-RCF2 [START_REF] Xin | Relational collaborative filtering: Modeling multiple item relations for recommendation[END_REF] is a hybrid method that combines item-based CF approach with knowledge graph embedding method to jointly learn a user-item preference model and an itemitem relational data model. Specifically in user-item preference model, they use a two-level hierarchy attention mechanism to capture the interactions between user embedding and relation types and the weights between users and historical items with specific relation values.

These baselines have not been designed to promote diversity. We use them to evaluate the accuracy of our approach before applying diversification to the recommended list. To ensure a fair comparison when evaluating diversification ability, we adopt a similar approach as our DivKG. We thus combine each algorithm with two baselines diversification techniques, namely MMR [START_REF] Carbonell | The use of mmr, diversity-based reranking for reordering documents and producing summaries[END_REF] and the method from [START_REF] Chen | Fast greedy map inference for determinantal point process to improve recommendation diversity[END_REF] that we denote FastDPP. MMR is a well-known re-ranking approach to promote diversity in recommendation, that iteratively re-ranks items to adjust the trade-off between accuracy and diversity. FastDPP promotes diversity by re-ranking the results using DPP and MAP inference. In total, we obtain 12 diversified baselines.

Finally, we also compare EMDKG with two recent baselines that consider DPP to provide diversity-promoting recommendations: DivKG [START_REF] Gan | Enhancing recommendation diversity using determinantal point processes on knowledge graphs[END_REF] (our proposal discussed above) is a re-ranking approach exploiting multiple relations of items using KGE to provide recommendations. It combines TransKG with FastDPP to enhance the diversity of the result list, but it does not explicitly encode diversity into the representations. [START_REF] Wu | Pdgan: Adversarial learning for personalized diversity-promoting recommendation[END_REF] is a diversified recommendation method which combines determinantal point processes with GAN [START_REF] Goodfellow | Generative adversarial nets[END_REF] framework to generate personalized and diverse recommendations without using the relations between items and other entities or knowledge graphs.

PD-GAN

For reproducibility sake, we provide our source code3 .

Performance Metrics

To assess the accuracy of the proposed method and the baselines, we consider standard metrics widely used in the field (e.g. [START_REF] Kabbur | Fism: Factored item similarity models for top-n recommender systems[END_REF][START_REF] Wang | Irgan: A minimax game for unifying generative and discriminative information retrieval models[END_REF]), namely Hit Ratio (Hit@n) and Normalized Discounted Cumulative Gain (NDCG@n). We take n = {5, 10, 20}.

As we explicitly consider categorical information for item diversity we evaluate diversity performance of recommendation results also using categorical information based metrics. Similar to [START_REF] Wu | Pdgan: Adversarial learning for personalized diversity-promoting recommendation[END_REF][START_REF] Cheng | Learning to Recommend Accurate and Diverse Items[END_REF][START_REF] Rodrygo | Selectively diversifying web search results[END_REF], we evaluate the diversity through these two metrics, namely 1. Category Coverage (CC@n) given by:

CC@n = 1 |U | |U | u=1 |C n u | |C| (16.4)
2. α-NDCG@n [START_REF] Charles | Novelty and diversity in information retrieval evaluation[END_REF] given by:

α-NDCG@n = 1 |U | |U | u=1 αDCG u @n αIDCG u @n (16.5)
where

αDCG u @n = n k=1 L l=1 J u kl (1 -α) q u l,k-1 log 2 (1 + k) (16.6)
with J u kl equal to the rating of the kth item in the list for user u if kth item belongs to the genre l otherwise 0. q u l,k-1 counts the number of items belonging to genre l up to the k -1 position in the list, which accompanying the constant α to modify the redundancy in the recommendation list. αIDCG u @n denotes the largest value of αDCG u @n which achieves the ideal diversification of recommendation lists. For the length n of recommendation list we take n = {5, 10, 20}.

General results

First, we evaluate the modified knowledge graph embedding part of EMDKG against baselines (before applying DPP MAP inference diversification). Table 16.3 shows the results of accuracy and diversity for each method on ML100K-IMDb dataset. We can Table 16.4 shows the results of accuracy and diversity on dataset Anime. Our proposals EMDKG-E and EMDKG-H outperform BPRMF and FISM in all metrics of accuracy and diversity. Compared to IRGAN, although IRGAN show comparable results or slightly better results in terms of accuracy, EMDKG-E and EMDKG-H win with a margin for most diversity metrics except for CC@20. Compared to TransKG E and TransKG H , EMDKG-E and EMDKG-H respectively have outperformed on accuracy and diversity. We have conducted pairwise t-test to confirm the result difference with confidence 99%. We show the impact of parameter α in Figure 16.1. We choose Hit@10 as accuracy metric and CC@10 and α-NDCG@10 as diversity metrics for each method combined with one of diversification methods MMR or FastDPP. And we demonstrate the results on these three metrics respectively in Figure 16.1(a), Figure 16.1 (b) and Figure 16.1(c). In each chart, we present the results of the corresponding metric for every method by varying the trade-off parameter α. We can see that by increasing the value α, accuracy metrics tend to increase for most methods combined with any of the diversification method while diversity metrics have tendency of increasing in most diversification combinations. In terms of accuracy, EMDKG demonstrates a huge advantage under various α compared to other baseline methods, except for DivKG and FISM. Besides, we can tell that the combinations of EMDKG and FastDPP maintain better their accuracy while decreasing the α compared to those with MMR. While EMDKG and DivKG have comparable results in accuracy, EMDKG improves diversity in terms of both CC and α-NDCG for both diversification methods. Compared to FISM, EMDKG wins with a large margin in terms of both CC@10 and α-NDCG.

In terms of diversity, EMDKG-H shows competitive results in both diversity and accuracy results compared to all other methods. While the combinations of IRGAN+MMR gains advantage of α-NDCG, it also presents much lower accuracy for Hit@10 and lower diversity for CC@10. And compared to DivKG (noted as TransH+DPP) and TransH+MMR, although our proposal does not gain a huge margin in terms of accuracy (still in general no worse than both of them), EMDKG-H +DPP and EMDKG-H +MMR bring obvious improvements for both diversity metrics when varying trade-off parameter α correspondingly.

In particular, we demonstrate the trade-off points for EMDKG methods combined with MMR and FastDPP diversification in Figure 16.3, Figure 16.4, Figure 16.5 and Figure 16.6. Also to demonstrate the enhancing performance we also compare the TransKG methods combined with MMR diversification and DivKG method in the figures. We mark the accuracy results in red and diversity results in blue. In Figure 16.3(up) the trade-off point (between Hit@10 and CC@10) for EMDKG-E -DPP is when trade-off parameter α . = 0.27, achieving Hit@10 0.23 and CC@10 0.545 while the trade-off point for EMDKG-E -MMR is when trade-off parameter α . = 0.59 achieving a Hit@10 0.21 and CC@10 0.538. Actually we can see the trade-off point for EMDKG-E -DPP is above the trade-off point for EMDKG-E -MMR, beating both accuracy metric (Hit@10) and diversity metric (CC@10). In a similar fashion, in Figure 16.3(down) the trade-off point of DivKG-E sits above the trade-off point of TransKG-E -MMR, meaning both advantages in accuracy (Hit@10) and diversity metric (CC@10) for DivKG-E. We can observe a similar results in Figure 16.4 when the diversity metric is chosen as α-NDCG. For EMDKG-H and DivKG-H we demonstrate the trade-off points in Figure 16.5 and 16.6, where similar results of achieving better trade-off between an accuracy metric and a diversity metric can be found compared to applying MMR diversification. Furthermore, the trade-off point between EMDKG-E(h) -DPP also is higher than the trade-off point of DivKG-E(H) as the scale of the axis for the charts are the same. This also demonstrate a direct improvement of EMDKG framework over DivKG.

Impact of candidate item set length M .

We show the impact of candidate item set length M for applying diversification methods in Fig. 16.2. The range of candidate item set length M is {20, 25, 30, 35, 40, 45}. To speed up the re-ranking and keep the accuracy performance, we select the top-M (M >N ) items from the prediction of each recommendation before diversification as candidate items for re-ranking. We can tell from these figures that EMDKG combined with FastDPP achieves stable results for both diversity and accuracy, while the combination with MMR may suffer from a loss of accuracy when increasing the size M of candidate item sets. Besides, EMDKG shows better results when varying the length M compared to DivKG and TransKG+MMR.

Discussion over diverse item set generation

The generation of diverse item set directly influences EMDKG co-learning representation results, and it is thus of importance to discuss this procedure in detail. Three points should be considered.

First, as we have described in Section 12.2, the procedure of diverse item set relies heavily on random selection, therefore to alleviate the randomizing effect, we set the random generation to a very large number (50000 times for each user, inspired by Monte-Carlo methods).

Another specific choice is the selection of the maximum number of diverse sets for each user. We have chosen 100 most diverse item sets for each user for two main reasons:

1. we only consider the most diverse item sets according to a diversity metric for our model. As this part of diversity information for item representation is most informative for learning item latent vectors.

2. for accelerating the process of EMDKG learning, the number of diverse item sets should not be too large.

Finally the diverse item set generation is influenced by the selection of diversity metrics. As we have presented in Section 12.2 the diversity metric can be selected among categoricalinformation based diversity metrics, e.g. CC, α-NDCG. We have conducted model learning with diverse item sets generated by both diversity metrics (CC and α-NDCG) and the reported results align with each other. Thus in figures shown above, we shown the results with diverse item sets generated with diversity metric CC.

Conclusions

In this part, we test two frameworks to address diversity-aware top-N recommendation problem. Our first proposal DivKG combines knowledge graph embedding methods (KGE) and DPP models for diversified prediction. The motivation behind using knowledge graphs lies in their ability to capture various relations between items, users, and auxiliary entities, providing a solid basis for understanding user's behaviour and improving recommendation quality. Moreover, knowledge graphs may facilitate the reasoning behind the recommendation process, making it more convincing. We leave this direction for our future work. In order to diversify the results of top-N recommendation, we further test our method on datasets to construct DPP kernels over KGE to facilitate diversified predictions. The construction of kernel provides an accuracy-diversity trade-off. Our evaluation results prove that such a combination is beneficial in terms of both accuracy and diversity.

In our second proposal EMDKG, we aim at learning representations for top-N recommendation to achieve better accuracy-diversity trade-off. From our perspective, the latter is not limited to only achieving both high accuracy and diversity, but should also be robust under different parameter settings. Thus, we propose a novel EM-schemed diversity-encoded knowledge graph embedding model EMDKG which incorporates Item Diversity Learning and Knowledge Graph Embedding for this purpose. We compare EMDKG with multiple state-of-art baseline methods before and after applying two diversification methods MMR and DPP. The results show that before diversification EMDKG can adjust accuracy and diversity to a better trade-off and after diversification EMDKG can outperform the baselines when varying the trade-off parameters and the candidate item set length. In all, EMDKG demonstrates better performance in terms of accuracy-diversity trade-off compared to competitive state-of-art works. Recommender systems have been prevalent for three decades and still remain among the active research topics. As accuracy-centered recommendations are not aligned completely with user satisfaction in reality, diversity has been brought in recommendation as anther goal to alleviate redundancy and filter bubble effects. In this dissertation, we concentrate on a diversified top-N recommendation problem, aiming at achieving recommendation with both high accuracy and high diversity for each user. With recent advancements in knowledge graph embedding methods where multi-type relations are mapped into latent vector spaces, capturing good graph structures and knowledge facts, we transfer this category of approaches into recommendation tasks. In the mean time, determinantal point processes have been widely studied and applied in various machine learning tasks for result diversification. Its natural advantage of both capturing item affinity and item diversity in the accompanying kernel matrix inspires us to incorporate it into knowledge graph embedding for achieving a both accurate and diverse top-N recommendation.

Therefore, in this dissertation we present our two contributions for diversified recommendations based on knowledge graph embedding methods and determinantal point processes. Our first diversified recommendation model DivKG combines knowledge graph embedding methods (KGE) and DPP models for diversified prediction. It proposes a novel approach to construct personalized DPP kernel matrix based on translation-based knowledge graph embedding for diversified top-N item lists. The new approach for the personalized DPP kernel matrix is a linear combination of user-item affinity matrix and item-item similarity matrix, both derived of entity and relation vectors from knowledge graph embedding representations. The motivation behind using knowledge graphs lies in their ability to capture various relations between items, users, and auxiliary entities, providing a solid basis for understanding user's behaviour and improving recommendation quality.

As we assume the item vectors learnt from knowledge graph embedding can capture well the correlation with other items in DivKG, our second diversified recommendation EMDKG however does not rely on this assumption and argues that item vectors solely based on knowledge graph embedding can not capture good enough diversity of item lists. Thus, we propose two module co-learning framework for learning diversity-aware knowledge graph embedding for top-N recommendation and suggest a learning procedure to optimize the representations.

We then test our models DivKG and EMDKG on real life datasets to prove the effectiveness of our proposals. The empirical results of DivKG shown in Section 16.1 demonstrate the capability of knowledge graph embedding methods to enhance recommendation accuracy. In order to diversify the results of top-N recommendation, we further test on datasets to construct DPP kernels over KGE to facilitate diversified predictions. The construction of kernel provides an accuracy-diversity trade-off. Our experimental results shown in Section 16.1 prove that such a combination is beneficial in terms of both accuracy and diversity.

For validating EMDKG, we evaluate whether the co-learning framework for top-N recommendation can achieve better accuracy-diversity trade-off. In our perspective, the latter is not limited to only achieve both high accuracy and diversity, but should also be robust under different parameter settings. We therefore compare EMDKG with multiple state-of-art baseline methods before and after applying two diversification methods MMR and FastDPP. The results in Section 16.2 show that before diversification EMDKG can adjust accuracy and diversity to a better trade-off and after diversification EMDKG can outperform the baselines when varying the trade-off parameters and the candidate item set length. In all, EMDKG demonstrates better performance in terms of accuracy-diversity trade-off compared to competitive state-of-art works.

Future Directions

For future directions, we first emphasize that there are still many interesting topics in diversified recommendation tasks, despite our contributions in this domain.

The first direction lies in extending the current offline evaluation to online evaluation using A/B testing [START_REF] Tamburrelli | Towards automated a/b testing[END_REF]. In our evaluation for DivKG and EMDKG, we use offline evaluation, consisting of first using collected datasets, then dividing the datasets into training/validation/testing parts and using training and validation datasets for finding the optimal model and finally measuring the performance on testing datasets. The offline evaluation procedure can measure the recommendation performance in a rather easy-to-conduct and repeatable fashion and is widely used in academics. In contrast, online evaluation is preferred by industrial practitioners as they argue it will reflect the true utility of recommendation algorithms. Especially, when considering multiple-goal recommendation, it is significant to verify how the multiple goals affect the de-facto CTR performance.

The second direction is to add aggregate diversity as another goal for diversified recommendation. As we have briefly introduced aggregate diversity in Section 8.1, aggregate diversity targets at offering a more balanced recommendation of items in the system and can alleviate effectively the long-tail effect. Items which are seldom interacted in history may still be of great value to a particular group of users, therefore achieving additional goal -aggregate diversity will uncover the potentials of these items on the "tail". Thus, a multi-task recommendation regarding accuracy, individual diversity and aggregate diversity is also of great concern and will bring benefit to both users and items in the recommender systems. Another direction of potential future work is explainability in recommender systems. There is a recent burst of research interest for explainable AI as intelligent services offered to users should gain trust through getting more transparent and explainable. Thus, for recommendation tasks which also rely hugely on user satisfaction including understanding how the recommending mechanism works, it seems rather apparent that explainability in recommender system should be the trend. Actually there exist already several streams of explainable recommendations in recent literature [START_REF] Park | Uniwalk: Explainable and accurate recommendation for rating and network data[END_REF][START_REF] Ren | Social collaborative viewpoint regression with explainable recommendations[END_REF][START_REF] Lu | Why i like it: Multi-task learning for recommendation and explanation[END_REF][START_REF] Liu | On interpretation of network embedding via taxonomy induction[END_REF][START_REF] Li | A capsule network for recommendation and explaining what you like and dislike[END_REF][START_REF] Balog | Transparent, scrutable and explainable user models for personalized recommendation[END_REF].

A trendy solution to provide explanations for recommendation is to use textual review data [START_REF] Ren | Social collaborative viewpoint regression with explainable recommendations[END_REF][START_REF] Lu | Why i like it: Multi-task learning for recommendation and explanation[END_REF] as opinions can be extracted from textual reviews and by jointly learning an accuracy-based recommendation and a NLP classification a recommendation with 100 viewpoints can be generated. Social relation information have also been used to provide explanations in recommendation settings [START_REF] Park | Uniwalk: Explainable and accurate recommendation for rating and network data[END_REF][START_REF] Ren | Social collaborative viewpoint regression with explainable recommendations[END_REF]. Apart from textual information and social relations, structural information are also taken into account in some works [START_REF] Liu | On interpretation of network embedding via taxonomy induction[END_REF][START_REF] Tao | The fact: Taming latent factor models for explainability with factorization trees[END_REF][START_REF] Shulman | Meta decision trees for explainable recommendation systems[END_REF] for generating explanations. Structural information or more particularly tree-structure can help generate fine-grained explanations in different explanation styles (statement, comparative).

In Figure 19.1, we demonstrate such a hierarchical tree structure characterizing categorical information on dataset Amazon Movie & TV1 . However such hierarchical structure requires heavy manual work as there exist no effective and accurate solutions to autogenerate such information. On the other hand, graphical structures including knowledge graphs are omnipresent and conserve a fine-grained explanation potentials as tree structure is one particular type of graphs. Furthermore, knowledge graphs naturally capture explainable units (the relational triplets) which is specially advantageous for a explainable recommendation. However, using graph structure to explain recommendations faces a huge challenge which lies on the complexity of graph structure itself, particularly when applying to a real-world scenario.

In Figure 19.2, we demonstrate an auto-generated category graph based on item categorical information on dataset Amazon Beauty. Amazon Beauty is a comparatively small dataset with already more than 100 categories (many of them overlap with others). Therefore, to leverage the graph information for recommendation requires an intelligent method to pinpoint non-overlapping elements (nodes and links) on the graph but we argue that the capability of graphs for conserving human-understandable knowledge weighs more and motivate us for finding a good solution to provide a more transparent and explanation recommendation. 102

  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.4 The original metadata of datasets ML-100k and IMDb. . . . . . . . . . . . 16.1 Comparison of EMDKG against state-of-the-art approaches on accuracy and diversity metrics when varying the trade-off parameter α on dataset ML100K-IMDb. (a) hit ratio@10 , (b) category coverage (CC)@10, (c) α-NDCG@10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.2 Comparison of EMDKG against state-of-the-art approaches on accuracy and diversity metrics when varying the candidate item list length (tradeoff parameter: 0.5) on dataset ML-100K. (a) hit ratio@10 , (b) category coverage (CC)@10, (c) α-NDCG@10. . . . . . . . . . . . . . . . . . . . . . 16.3 Pairwise comparison of EMDKG-E -DPP and EMDKG-E -MMR on accuracy and diversity metrics . . . . . . . . . . . . . . . . . . . . . . . . . 16.4 Pairwise comparison of DivKG-E and TransKG-E -MMR on accuracy and diversity metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.5 Pairwise comparison of EMDKG-H -DPP and EMDKG-H -MMR on accuracy and diversity metrics . . . . . . . . . . . . . . . . . . . . . . . . . 16.6 Pairwise comparison of DivKG-H and TransKG-H -MMR on accuracy and diversity metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.1 Categorical tree extracted from categorical information on dataset Amazon Movie & TV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.2 The category graph based on item categorical information on dataset Amazon Beauty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7. 1

 1 List of Triplets in part of MovieLens data, corresponding to Figure. 7.1 . . 11.1 The construction of personalized kernel matrix for DPP. For a user having

  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . : How can we incorporate knowledge graph embedding for a recommendation with multiple types of information? . . . . . . . . . . . . . . . . 3.2 RQ2: How can we combine knowledge graph embedding results with diversification methods? In particular, how can we incorporate knowledge graph embedding with determinantal point processes for a top-N recommendation? 3.3 RQ3: How can we evaluate the performance of a diversified recommendation? 4 Publications and Communications 4.1 International publications . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 National publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Scientific Communications . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 6 . 1 :

 61 Figure 6.1: A content-based filtering method create user profiles from historical preferred items' content and a recommendation can be generated by finding similar items to user profile.

  are mapped into latent space as latent vectors and shown in the right part of the Figure.7.1.

Figure 7 . 1 :

 71 Figure 7.1: On the left, there is a knowledge graph for part of MovieLens data, includingentities (movies, staff working for the movies, genres) and relations connecting the entities (InActorOf, IsInGenre etc.). On the right it is the latent embedding space where both entities and relations are embedded into. Knowledge graph embedding methods map elements of a knowledge graph (including both entities and relations) into the latent space while conserving the graph structure(node similarity etc.).

  w r ∈ C d and Re(•) denotes the real part of a complex value. It is customary to represent the real part and imaginary part separately for a complex value, so for each entity e, we let Re(v e ) ∈ R d and Im(v e ) ∈ R d represent the real and imaginary parts. And for each relation r, we also let Re(v r ) ∈ R d and Im(v r ) ∈ mathbbR d represent the real and imaginary parts of r. As we have in ComplEx, v e = Re(v e ) + Im(v e )i, v r = Re(v r ) + Im(v r )i (7.4) and i 2 = -1,we can rewrite Eq. 7.3 into such,

  de×dr×de and d e and d r are the dimensions of entity and relation vectors separately.

Figure 7 . 2 :

 72 Figure 7.2: Simple illustrations of TransE and TransH. Source: [15].

Figure 7 . 3 :

 73 Figure 7.3: A simple illustration of TransD. Source: [69].

  is a tensor related to relation r, and V r ∈ R k×2d , u r ∈ R k and b r ∈ R k are all parameters related to relation r to express interaction of the entities through relation in the triplet.

  .24) where v l e is the entity representation in layer l and v l+1 e is the entity representation in layer l + 1 for entity e. σ(•) is an activation function, and W l is the model parameter for layer l. m l+1 e is given by the formula as such, where N (•) represents the neighbors (other entities with an edge with entity e in the original graph structure) of entity e and it represents the average of neighbor nodes of entities e in layer l.

  l+1 are all model parameters to transfer entity/relation vectors from layer l to l + 1.KE-GCN[START_REF] Yu | Knowledge embedding based graph convolutional network[END_REF], compared to CompGCN, replaces the composition operators in m l+1 e update to a differential form and the item propagate from layer l to l + 1 is given as,

Figure 8 . 1 :

 81 Figure 8.1: An example of long-tail effect distribution chart. The horizontal axis represents the number of items in this distribution; and the vertical axis represents the occurrences of searches for items. The pink area on the left is the dominant "head" of the distribution while the green area shows a long tail of huge number of items with low searches.

  u,v∈S d(u, v), which can be formulated as arg max f (S) + λ {u,v}:u,v∈S d(u, v) (8.14) subject to | S |= p, with d(•, •) a metric distance function on item sets. Then they propose one greedy-based solution and one local search solution for this task with an approximation ratio of 2.

Definition 7 .

 7 (Category Coverage, CC) Given a ground item feature set F and a list of items I equipped with their item feature list F I = {F i |i ∈ I}, the category coverage (CC) is formulated as,CC : f ∈F 1 f (∪F I ) |F|(10.5)where, | • | represents the cardinality of a set and 1 is an indicator function.

Definition 8 .

 8 (Intra-List Diversity, ILD) Given a list of items I and a pair-wise distance function dist(•, •) defined over items, the intra-list diversity is formulated as, ILD I = i∈I j∈I∧i̸ =j dist(i, j) (10.9)

Figure 11 . 1 :

 111 Figure 11.1: DivKG: a diversity enhancing recommendation framework based on knowledge graph embedding methods. Datasets are preprocessed to extract entityrelation triplets for constructing knowledge graphs for recommendation. Then given such a knowledge graph, we learn the vectorial representations of entities and relations by applying different knowledge graph embedding methods.After obtaining the latent vectors of users, items, other entities and relations, personalized kernel matrix can be constructed for each user. Finally we render each user a diversified recommendation list of items by the fast greedy MAP inference algorithm on its corresponding kernel matrix.

  Figure 11.2 demonstrates an example of such a knowledge graph structure in movie recommendation scenario.

Figure 11 . 2 :

 112 Figure 11.2: An example of knowledge graph for movie recommendation, reflecting different relations (Interaction, IsGenreOf, IsDirectorOf, IsPlayedBy) between various entities (user, item, genre, director, actress). Such a knowledge graph is an extension of user-item interaction used by collaborative filtering methods.

Figure 11 . 3 :

 113 Figure 11.3: The iterative process of selecting items by FastDPP. Y g is the dynamic item set containing the items already selected by FastDPP and is initialized as an empty set ∅. When the number of items in Y g has not reached N , FastDPP updates Y g by selecting an item j among all the unselected candidate items which maximizes logdet(L Yg∪{i} ) -logdet(L Yg ).

Figure 12 . 1 :

 121 Figure 12.1: This is the general structure of EMDKG, composed of two modular learning: the Item Diversity Learning and Knowledge Graph Embedding.

8 : 9 :

 89 Sort RandomSet by Div(•) value in descend order Append top pairs from RandomSet to T 10: end for 12.3 Item Diversity Learning.

Figure 12 . 2 :

 122 Figure 12.2: A demonstration of how Item Diversity Learning module works.

5 )

 5 which is equivalent to the log-determinant of submatrix A on a new kernel L u = Diag(exp(βQ(u))) • LDiag(exp(βQ(u)))(12.6)

Figure 15 . 2 :

 152 Figure 15.2: Correlation of genres on dataset ML100K and Anime. (a) the correlation of 19 movie genres based on genre distribution of items on dataset ML100K; (b) the correlation of 44 genres based on genre distribution of items on dataset Anime.

Figure 15 . 3 :

 153 Figure 15.3: Anime genre count over all items on dataset Anime in descending order.The anime genres are comedy, action, fantasy, sci-fi, drama, shounen, kids, romance, school, slice of life, hentai, supernatural, mecha, music, historical, magic, ecchi, shoujo, seinen, sports, mystery, super power, military, parody, space, horror, harem, demons, martial arts, dementia, psychological, police, game, samurai, vampire, thriller, cars, shounen ai, shoujo ai, josei, yuri, yaoi, and other.

Figure 15 . 4 :

 154 Figure 15.4: The original metadata of datasets ML-100k and IMDb.

Figure 16 . 1 :Figure 16 . 2 :

 161162 Figure 16.1: Comparison of EMDKG against state-of-the-art approaches on accuracy and diversity metrics when varying the trade-off parameter α on dataset ML100K-IMDb. (a) hit ratio@10 , (b) category coverage (CC)@10, (c) α-NDCG@10. see that EMDKG-E and EMDKG-H perform much better for all accuracy and diversity metrics compared to BPRMF. Compared to FISM, although its performance in term of accuracy shows a slight advantage (not statistically significant), EMDKG-E and EMDKG-H bring a significant improvement in diversity. Although IRGAN and RCF show higher values in terms of CC@10 and CC@20, EMDKG-E and EMDKG-H still defeats these two methods in other diversity metrics and largely in accuracy. Compared to TransKGs, it is observed that TransKG H outperforms EMDKG-E and EMDKG-H in terms of accuracy but EMDKG-H compensates it by an obvious gain in diversity w.r.t. all diversity metrics. Besides, EMDKG-E shows both improvements in accuracy and diversity comparing to TransKG E .

Figure 16 . 3 : 93 Figure 16 . 4 : 94 Figure 16 . 5 : 95 Figure 16 . 6 :

 163931649416595166 Figure 16.3: Pairwise comparison of EMDKG-E -DPP and EMDKG-E -MMR on accuracy and diversity metrics

Figure 19 . 1 :

 191 Figure 19.1: Categorical tree extracted from categorical information on dataset Amazon Movie & TV.

Figure 19 . 2 :

 192 Figure 19.2: The category graph based on item categorical information on dataset Amazon Beauty.

  An example of knowledge graph for movie recommendation, reflecting different relations (Interaction, IsGenreOf, IsDirectorOf, IsPlayedBy) between various entities (user, item, genre, director, actress). Such a knowledge graph is an extension of user-item interaction used by collaborative filtering methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 The iterative process of selecting items by FastDPP. Y g is the dynamic item set containing the items already selected by FastDPP and is initialized as an empty set ∅. When the number of items in Y This is the general structure of EMDKG, composed of two modular learning: the Item Diversity Learning and Knowledge Graph Embedding. . . . . . . 12.2 A demonstration of how Item Diversity Learning module works. . . . . . . 15.1 Movie genre count over all items on dataset ML100K in descending order.(19 genres including Other in total) . . . . . . . . . . . . . . . . . . . . . . . . 15.2 Correlation of genres on dataset ML100K and Anime. (a) the correlation of 19 movie genres based on genre distribution of items on dataset ML100K; (b) the correlation of 44 genres based on genre distribution of items on dataset Anime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.3 Anime genre count over all items on dataset Anime in descending order.

g has not reached N , FastDPP updates Y g by selecting an item j among all the unselected candidate items which maximizes logdet(L Yg∪{i} ) -logdet(L Yg ). . . . . . . . . . . . . . . . 12.1

41 8 Diversity-Aware Information Retrieval and Recommendation

6 Recommender Systems 6.1 Content-Based Filtering Recommender Systems . . . . . . . . . . . . . . . 6.2 Collaborative Filtering Based Recommender Systems . . . . . . . . . . . . 6.3 Hybrid Recommender Systems . . . . . . . . . . . . . . . . . . . . . . . . . 7 Knowledge Graph Embedding and KGE Based Recommendation 7.1 Tensor Decomposition Based Knowledge Graph Embedding . . . . . . . . . 7.2 Translation Based Knowledge Graph Embedding . . . . . . . . . . . . . . . 7.3 Deep Neural Network Based Knowledge Graph Embedding . . . . . . . . . 7.4 KGE-Based Recommendation . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Diversification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  1 , t i,2 , ..., t i,l }. The similarity between a term t i,k and an item content Content(i) is denoted as w i,k , i ∈ {1, 2, ..., |I|} , k ∈ {1, 2, ..., l} and can be written as,

	w i,k =	TF -IDF(t i,k , Content(i)) k=l k=1 TF -IDF(t i,k , Content(i)) 2	(6.1)
	which is a normalized TF-IDF between the term t i,k and item content Content(i). And
	the TD-IDF of t i,k and Content(i) is formulated as,
	TF -IDF(t i,k , Content(

  Thus, the learning of user profiles is to learn a two-class classification model with labeled historical items with their content represented by a collection of weighted term vectors as training dataset. One of the most common used methods for this two-class classification task is Naïve Bayes classifiers. In CBF settings, Naïve Bayes is a probabilistic model which estimates the a posteriori probability P (c|d) of the a document d belonging to the class c, c ∈ {c + , c -}.c + and c -represent separately the positive and negative category. According to the Bayes theorem, the a posteriori probability P (c|d) can be written as,

	P (c|d) =	P (c)P (d|c) P (d)	(6.4)
	where P (d|c) is the probability of seeing document d given a class c and P (c) is the
	probability of observing documents in category c. As P (d) represents the probability of
	observing document d and is the same for either c + or c -, so to decide which category
	document d falls in, we choose the category ĉ by such rule,
	ĉ = argmax c i P (c i )P (d|c i )	(6.5)
	To estimate P (d|c i ), c i ∈ {c -, c + }, the Naïve Bayes classifier uses an independence assump-
	tion: all terms in a document d are mutually independent, conditional on c i . Thus,
	P (c|d i ) = P (c|t i1 , t i2,..,t il )	(6.6)

Table 7 .

 7 Table. 7.1 1: List of Triplets in part of MovieLens data, corresponding to Figure. 7.1

	Head	Relation	Tail
	Toy Story	IsInGenre	Comedy
	Toy Story	IsInGenre	Animation
	Toy Story	IsInGenre	Children's
	nm0169505	IsWriterOf	Toy Story
	nm0169505	IsWriterOf	Money Talks
	nm0000158	IsActorIn	Toy Story
	nm0000158	IsActorIn	Philedelphia
	Money Talk	IsInGenre	Comedy
	Philedelphia	IsInGenre	Drama
	Babe	IsInGenre	Drama
	Babe	IsInGenre	Children's
	nm0922806	IsComposerOf	Babe
	nm0922806	IsComposerOf Children of the Revolution
	Children of the Revolution	IsInGenre	Comedy

Based Diversified Recommendations 9 Introduction 10 Background

10.1 Diversity Metrics for Recommendation . . . . . . . . . . . . . . . . . . . . 10.2 Determinantal Point Processes . . . . . . . . . . . . . . . . . . . . . . . . . 10.3 Translation-Based Knowledge Graph Embedding for Recommendation . . . 11 DivKG: Improving Diversity for Recommendation Based on Knowledge Graphs 11.1 Knowledge Graph Embedding for Entity and Relation Representations . . 11.2 Diversity-Aware Recommendation on Determinantal Point Processes . . . .

12 EMDKG: Diversity-Aware Representation Learning for a Better Trade-off Diversified Recommendation 12

  Modified Translation-Based Knowledge Graph Embedding for Recommendation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.5 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

	13 Conclusion

.1 General Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2 Diverse Item Sets Generation . . . . . . . . . . . . . . . . . . . . . . . . . 12.3 Item Diversity Learning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.4

Definition 9. Diversity-Aware Knowledge Graph Embedding

  Knowledge graph embedding methods represent both entities and relations of the knowledge graphs into vectors, v e , e ∈ E and v r , r ∈ V accordingly.And a vectorial diversity measure div v : R n×d → R defined on a subset of v E is given for n k-dimension vectors. M is a subset of E where a semantic diversity measure is defined div s : 2 M → R. An optimum diversity-aware knowledge graph embedding should obey the following rule: For subsets

. (E, V, A, R) is defined as a knowledge graph, with E a set of entities, V ⊂ E × E the edges connecting the entities E; A is a mapping function A : E → T with T a finite set of entity types and R is also a mapping function R : V → S with S a finite set of relation types.

  this part, we have presented our two models to diversified recommendations based on knowledge graph embedding methods. Our first diversified recommendation model DivKG proposes a new approach to construct personalized DPP kernel matrix based on translation-based knowledge graph embedding results for diversified item lists. The new approach for the personalized DPP kernel matrix is composed of user-item affinity matrix and item-item similarity matrix, both derived of entity and relation vectors from knowledge graph embeddings. In DivKG we assume the item vectors learnt from knowledge graph embedding can capture well the co-relation with other items. Our second diversified recommendation EMDKG however does not rely on the assumption that item vectors solely based on knowledge graph embedding can capture good enough diversity of item lists. And we propose double-module framework for learning diversity-aware knowledge graph embedding for top-N recommendation and use a co-learning to optimize the representations.Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.2 Evaluation Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experiments on DivKG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.2 Experiments on EMDKG . . . . . . . . . . . . . . . . . . . . . . . . . . . .

	Part IV
	Evaluation
	14 Introduction
	15 Experimental Settings
	15.1 16 Experiment Results
	16.1

Table 16 .

 16

	1: Accuracy results before diversification with dimension=75, learning rate=0.001
	on dataset ML100K-IMDb.
			Hit			NDCG
	Metric	@5	@10	@20	@5	@10	@20
	BPRMF 0.1394 0.2200 0.3240 0.0888 0.1150 0.1412
	FISM	0.1182 0.2041 0.3160 0.0746 0.1023 0.1304
	RCF	0.1442 0.2179 0.3261 0.0888 0.1123 0.1393
	TransE 0.1879 0.2842 0.4087 0.1253 0.1561 0.1876
	TransH 0.1917 0.2861 0.4123 0.1257 0.1561 0.1878

Table 16

 16

.1 we demonstrate the accuracy results of the methods used in DivKG (TransE and TransH) against baseline methods on metrics MRR and NDCG before diversification.

Table 16 .

 16 2: Diversified recommendation results with α=0.9 on dataset ML100K-IMDb.

	Metric	Hit@10 NDCG@10 ILAD	ILMD
	BPRMF+MMR	0.2821	0.0789	0.9683 0.8867
	BPRMF+FastDPP 0.3065	0.0848	0.9922 0.9726
	RCF+MMR	0.2842	0.0785	0.9698 0.8886
	RCF+FastDPP	0.3001	0.0798	0.9923 0.9729
	TransE+MMR	0.2768	0.0774	0.9911 0.9183
	DivKG E	0.3160	0.1176	0.9959 0.9768
	TransH+MMR	0.2693	0.0705	0.9898 0.8951
	DivKG H	0.3175	0.1178	0.9956 0.9690
	Table

Table 16 .

 16 2 shows diversified recommendation performance w.r.t. both accuracy and diversity metrics. It can be seen that our methods DivKG E and DivKG H that combine FastDPP with TransE and TransH respectively outperform baselines methods w.r.t. both, accuracy and diversity. Almost all accuracy-based methods combined with FastDPP outperform those combined with MMR.

Table 16 .

 16 3: Accuracy and diversity results before diversification method for ml100k extended datasets. Bold results are significantly higher than other results in the same column with p = 0.01.

	Metrics	@5	Hit (%) @10	@20	@5	NDCG (%) @10	20	@5	CC (%) @10	@20	@5	α-NDCG (%) @10	20
	BPRMF	8.91	17.71	32.03	5.51	8.34	11.93	34.96	49.51 65.32	39.78	51.61	62.96
	FISM	22.87	31.44	42.82	15.47	18.23	21.09	36.57	50.21 63.47	39.73	51.73	62.31
	IRGAN	10.55	16.50	23.45	6.99	8.91	10.65	37.17	53.26 69.18	37.55	51.92	64.74
	RCF	12.20	19.51	29.59	7.51	9.86	12.39	37.14	53.40 69.88	38.60	52.71	65.86
	TransKG E	22.07	32.43	46.49	14.25	17.57	21.13	36.18	50.87 65.73	41.83	53.85	65.14
	TransKG H	23.38 34.36 47.01 15.70 19.24 22.44	36.05	50.93 65.65	41.50	53.77	64.95
	EMDKG-E	22.12	33.65	46.03	14.59	17.97	21.32	36.45	51.22 66.24	42.00	54.23	65.58
	EMDKG-H	22.08	33.01	46.34	14.08	17.60	20.95	37.34	52.15 66.67 43.27 55.50 66.66

Table 16 .

 16 4: Accuracy and diversity results before diversification method for anime datasets. Bold results are significantly higher than other results in the same column with p = 0.01.

	Metrics	@5	Hit (%) @10	@20	@5	NDCG (%) @10	@20	@5	CC (%) @10	@20	@5	α-NDCG(%) @10	@20
	BPRMF	8.13	11.56	17.81	5.13	6.25		7.83	22.95	34.23	46.46	23.95	32.06	40.21
	FISM	11.72	17.03	22.97	7.29	8.98	10.48	24.95	37.31	50.43	25.63	34.26	42.97
	IRGAN	14.84	19.38	24.06	9.79	11.30	12.46	26.28	35.63	52.43	27.97	34.89	44.95
	RCF	13.02	16.37	19.22	7.46	9.01	11.20	26.80	38.99	51.97	28.10	34.94	45.33
	TransKG E	14.38	20.00	25.63	9.37	11.00	12.54	26.64	39.56	52.09	29.41	38.47	47.30
	TransKG H	13.44	20.00	26.88	9.06	11.02	12.89	26.70	39.77	52.21	29.52	38.66	47.31
	EMDKG-E	14.84 20.16	26.25	9.72 11.42	12.89	26.65	39.40	51.50	29.14	38.08	46.77
	EMDKG-H 14.84	19.22	27.34	9.64	11.05	13.08 27.00 40.66	51.60	29.49 38.94	47.14

16.2.4 Impact of trade-off parameter α.

Cette thèse est accessible à l'adresse : https://theses.insa-lyon.fr/publication/2022LYSEI047/these.pdf © [L. Gan], [2022], INSA Lyon, tous droits réservés

IMDb datasets link: https://datasets.imdbws.com/

Anime datasets link: https://www.kaggle.com/datasets/CooperUnion/anime-recommendationsdatabase

The source code for IRGAN: https://github.com/geek-ai/irgan

https://github.com/XinGla/RCF

https://github.com/LGanShare/EMDKG_WI.git

The Amazon dataset can be found here: https://nijianmo.github.io/amazon/index.html

Remerciements

Data Mining, KDD '16, page 353-362, New York, NY, USA, 2016. Association for Computing Machinery.

DivKG: Improving Diversity for Recommendation

Based on Knowledge Graphs

In this chapter, we present our first diversity-enhancing recommendation framework -DivKG to make recommendations combining knowledge graph embeddings (step 1) and determinantal point processes (DPP) prediction (step 2). Given a knowledge graph for recommendation, we first apply knowledge graph embedding methods to learn the representations of entities engaged in the recommendation (including users and items) then we present a new approach to construction DPP personalized kernel matrix based on the learnt vectors from knowledge graph embedding. Finally we generate and provide top-N diversified recommendation by applying a fast greedy Maximum A Posteriori (MAP) Inference algorithm on each kernel matrix. We present a visualized procedure of our framework in Figure 11.1. than 947K films. We demonstrate a diagram of metadata of these two datasets in Figure .  15.4.

We process these two datasets as follows. For the rating information from ML-100K, we follow traditional idea to binarize explicit rating data by keeping the ratings score >= 4 or higher and interpret them as implicit feedback. And for item-side auxiliary information, we extract 13 categories of information from IMDb, namely: movie genre, self (where the actor/actress plays himself/herself in the movie), director, cinematographer, composer, producer, editor, actor, actress, writer, production designer, archive footage, and archive sound. We combine these data with MovieLens dataset for constructing multi-relation datasets, using the extracted categories to determine the relations within our knowledge graph. We denote the constructed multi-relation dataset as ML100K-IMDb. In Figure 15.1, we demonstrate the statistics of the genre information over total users, while observing a unbalanced distribution of genre information over total items. We also demonstrate in Figure 15.2(a), the correlation of different genres are shown in the heatmap, where the correlation between genres are in general not so significant. We also use Anime dataset 2 which contains 5+ million 10-grades ratings from 73,516 users on 12,294 animes. For Anime datasets, we are only given genre information as auxiliary information for constructing the knowledge graph; each anime may belong to one