Siying Li
email: siying.li@utc.fr

Marie-Hélène Abel
email: marie-helene.abel@utc.fr

Elsa Negre
email: elsa.negre@dauphine.fr

Analyzing performances of three context-aware

Keywords: Context-aware recommendations, Collaborator, Collaboration context, Ontology-based semantic similarity

come

Introduction

With the development of information technology, increasingly more collaborative tools have been provided for users' remote collaborations. This makes it difficult for users to organize and manage the heterogeneous information among these tools within collaborations. Particularly, users find it difficult to retrieve information about collaborators and therefore cannot work with appropriate collaborators to advance their collaborations. To help users make decisions about collaborators, recommender systems (RS) are designed and applied [START_REF] Nunes | A systematic review and taxonomy of explanations in decision support and recommender systems[END_REF], which can generate collaborator recommendations for them. However, such recommendations are sometimes not quite relevant, due to the missing consideration of context [START_REF] Adomavicius | Context-aware recommender systems[END_REF]. For instance, while generating collaborator recommendations, information of user's collaboration place and time should also be considered, which can influence users' needs for their collaborators. To incorporate context into recommendation generation processes, a new type of RS has been proposed: Context-Aware Recommender System (CARS). Despite the quick development of CARS, there is little studies on analyzing and evaluating the performance of different context-aware recommendation algorithms.

Therefore, we are interested in testing, analyzing, and evaluating the performance of our three proposed context-aware collaborator recommendation algorithms (i.e., PreF1, PoF1, and PoF2) [START_REF] Li | Ontology-based semantic similarity in generating context-aware collaborator recommendations[END_REF] in terms of accuracy and time efficiency. The three algorithms all consider and compare the context of collaboration by means of ontology-based semantic similarity to generate context-aware collaborator recommendations for users. Their differences lie in where and how the semantic similarities are applied in recommendation generation processes. Specifically, PreF1 employs semantic similarities in the pre-processing step, following contextual pre-filtering approach [START_REF] Adomavicius | Context-aware recommender systems[END_REF]. As for PoF1 and PoF2, they utilize semantic similarities in post-processing step, based on contextual post-filtering approach [START_REF] Adomavicius | Context-aware recommender systems[END_REF]. Besides, all the three algorithms can be realized and tested in a public dataset of scientific collaborations. This allows us to evaluate their performances through three metrics: F1, mean absolute error, and execution time. These results then make it possible to analyze both advantages and disadvantages of the three algorithms in producing context-aware collaborator recommendations.

The remainder of this paper is constructed as follows. Section 2 studies context-free and context-aware recommender systems. Section 3 presents our contributions in (i) developing three context-aware collaborator recommendation algorithms (i.e., PreF1, PoF1, and PoF2) based on a collaboration context ontology and an ontology-based semantic similarity, (ii) applying a dataset to test them, (iii) analyzing and comparing their performances in terms of accuracy and time efficiency through three metrics. We then discuss the strengths and weaknesses of the three context-aware collaborator recommendation algorithms in Section 4. Finally, some conclusions and future work are shown in Section 5.

Related Work

This section distinguishes context-free and context-aware recommender systems (RS). Section 2.1 and 2.2 separately explore the approaches and techniques that can be used in these RSs. We then discuss their differences and relationships in Section 2.3.

Context-free recommender systems

Context-free RSs3 gather and utilize two types of information to provide recommendations: user and item [START_REF] Ricci | Introduction to recommender systems handbook[END_REF]. Here, item is the general term to indicate the objects that 2D RS recommends to users, while user indicates people who will receive these recommendations [START_REF] Ricci | Introduction to recommender systems handbook[END_REF]. For example, in a collaborator RS, an item indicates a collaborator. Particularly, an item is characterized and sorted by its ratings that indicate how a particular user liked/preferred this item [2] [21]. Thus, the core task of 2D RSs is: Given an initial set of ratings that users explicitly or implicitly give for items, 2D RSs try to predict users' unknown ratings for items and decide which items to recommend [3] [21]. Specifically, users' ratings for items in a 2D RS can be calculated by a function as follows [START_REF] Adomavicius | Toward the next generation of recommender systems: A survey of the state-of-the-art and possible extensions[END_REF]:

R RS : U ser × Item → Rating (1)
where Rating is a totally ordered set (e.g., non-negative integers or real numbers within a certain range).

Based on the literature review, there are four main approaches to generate 2D recommendations [START_REF] Adomavicius | Incorporating contextual information in recommender systems using a multidimensional approach[END_REF] [2] [21]:

1) Content-Based filtering (CB) approach first creates a profile for each user and a description for each item, then predicts users' unknown ratings by comparing these user profiles and item descriptions [1] [2]. Usually, CB approaches apply and implement the following techniques: Vector Space Model (VSM), TF-IDF, Semantic Analysis (using ontology) [START_REF] Middleton | Ontological user profiling in recommender systems[END_REF], Naïve Bayes, Decision Trees [START_REF] Lops | Content-based recommender systems: State of the art and trends[END_REF], Neural Networks [START_REF] Van Den Oord | Deep content-based music recommendation[END_REF], Cosine similarity [START_REF] Lops | Content-based recommender systems: State of the art and trends[END_REF]. 2) Collaborative Filtering (CF) approach predicts a particular user's unknown rating for an item based on the user's past behaviors, such as previous transactions and items' ratings [START_REF] Adomavicius | Incorporating contextual information in recommender systems using a multidimensional approach[END_REF]. The general assumption of CF approach is: if two users have same rating on one item, one of them is more likely to have the similar rating as the other on a different item [1] [2]. In CF approaches, the applicable techniques include Nearest neighbor [START_REF] Sarwar | Item-based collaborative filtering recommendation algorithms[END_REF], Pearson correlation [START_REF] Jin | An automatic weighting scheme for collaborative filtering[END_REF], Cosine similarity [START_REF] Desrosiers | A comprehensive survey of neighborhood-based recommendation methods[END_REF], similarities in ontology [START_REF] Zhang | Ontology-based collaborative filtering recommendation algorithm[END_REF], Matrix Factorization (MF), Latent Dirichlet Allocation (LDA), Singular Value Decomposition (SVD) [START_REF] Koren | Advances in collaborative filtering[END_REF]. 3) Knowledge-Based (KB) approach utilizes specific domain knowledge about users' requirements and preferences to generate 2D recommendations [START_REF] Felfernig | Developing constraint-based recommenders[END_REF]. Such approaches either determine unknown ratings by evaluating similarity metrics between the predefined cases and users' requirements [START_REF] Bridge | Case-based recommender systems[END_REF], or estimate the extent to which an item can meet users' explicit requirements based on certain rules in a predefined knowledge base [START_REF] Felfernig | Developing constraint-based recommenders[END_REF]. For KB approaches, techniques related to knowledge base and similarity measurement can be used and implemented, such as ontologies [START_REF] Tarus | Knowledge-based recommendation: a review of ontology-based recommender systems for e-learning[END_REF] and semantic similarity [START_REF] Sánchez | Ontology-based semantic similarity: A new feature-based approach[END_REF]. 4) Hybrid approach combines two or more other previous approaches (i.e., CB, CF, and KB) to predict users' unknown ratings for items [START_REF] Adomavicius | Toward the next generation of recommender systems: A survey of the state-of-the-art and possible extensions[END_REF]. Thus, the techniques that can be used in the three previous approaches are also applicable in Hybrid approaches.

Context-aware recommender system

As for Context-Aware Recommender System (CARS), it is constructed by incorporating context into 2D recommendation generating process, resulting in more accurate recommendations [START_REF] Palmisano | Using context to improve predictive modeling of customers in personalization applications[END_REF]. Unlike 2D RS, CARS deals with at least three types of information: user, item and context. It is even possible to construct a CARS using more types of information. For example, a context-aware movie RS [START_REF] Adomavicius | Incorporating contextual information in recommender systems using a multidimensional approach[END_REF] handled information separated into 5 dimensions: user, item, place, time and companion. Thus, the rating function of a n-dimensional CARS is [START_REF] Adomavicius | Incorporating contextual information in recommender systems using a multidimensional approach[END_REF]:

R CARS : D 1 × D 2 × ... × D n → Rating(n ≥ 3, n ∈ N * ) (2)
where D 1 , D 2 , ..., D n represent n dimensions of information (including user, item, context, ...). When n = 3, it becomes: U ser × Item × Context → Rating. Particularly, [START_REF] Adomavicius | Context-aware recommender systems[END_REF] proposed three approaches to incorporate the context in different steps of recommendation processes (see Fig. 1)4 , as follows:

-Contextual pre-filtering (PreF) approach first applies the context to filter ratings that are irrelevant to specific contexts [START_REF] Adomavicius | Incorporating contextual information in recommender systems using a multidimensional approach[END_REF]. It then employs -Contextual modeling (CM) approach produces truly multidimensional recommendations. It deals with all dimensions of information (i.e., D 1 , D 2 , D 3 , ..., D n ) in each step of the whole recommendation generation process.

Discussion

Based on the literature review of 2D RS and CARS, the techniques of CARS are still immature when compared to those of 2D RS. However, there is something in common between them. For example, techniques of some 2D recommendation approaches can directly serve in PreF and PoF approaches. This indicates that 2D recommendation approaches are important sources of inspiration for CARS, thus contributing to their development. Specifically, both PreF and PoF approaches can support any 2D recommendation approaches (i.e., CB, CF, KB, and Hybrid), but they require extra steps in generating context-aware recommendation: PreF needs to first filter out irrelevant ratings, as pre-processing step; PoF must filter out irrelevant 2D recommendation results, as post-processing step (see Fig. 1). Besides, CM approach necessitates more complicated rating functions to deal with all dimensions of information in the recommendation generation process (see Fig. 1). Consequently, any 2D recommendation approaches can not be directly applied in CM.

Moreover, the multidimensional information in CARS also causes difficulties: from the perspective of information volume, CM can not handle the same amount of users and items as the other two approaches (i.e., PreF and PoF). While CM needs to process information of D 1 ×D 2 ×...×D n , the other two focus only on information of D 1 × D 2 . Meanwhile, as the dimensions of the information increase, the computational complexity of CM becomes higher and higher. However, for PreF and PoF, only their extra steps (pre-processing and post-processing) become more complicated. This indicates that, unlike PreF and PoF, CM is too costly when information volume and complexity are heavy. Thus, we concentrate on using PreF and PoF approaches to develop three context-aware collaborator recommendation algorithms (i.e., PreF1, PoF1, and PoF2) [START_REF] Li | Ontology-based semantic similarity in generating context-aware collaborator recommendations[END_REF]. Particularly, PreF1 follows PreF approach, while PoF1 and PoF2 are built on PoF approach.

Contributions

This section first presents three context-aware collaborator recommendation algorithms that are developed based on a collaboration context ontology and an ontology-based semantic similarity. Then a public dataset of scientific collaborations is applied in two types of experiments to test and analyze the performances of these algorithms in terms of accuracy and time efficiency.

Context-aware collaborator recommendation algorithms

The collaboration context ontology MCC [START_REF] Li | Towards a collaboration context ontology[END_REF] employs a subject and its involved semantic 3-uples (i.e., <Subject, Predicate, Object>) to define a collaboration and its context. Specifically, a subject indicates a particular collaboration, while the related predicates and objects refer to its context which is represented by different dimensions. Thus, a collaboration c and its context are considered as a collection of semantic 3-uples with a single subject c in MCC.

Within such collections of semantic 3-uples, an ontology-based semantic similarity was proposed to measure the closeness between two collections [START_REF] Li | Ontology-based semantic similarity in generating context-aware collaborator recommendations[END_REF], which respectively represent two collaborations (c and d) and their contexts. This semantic similarity is calculated by the following equation [START_REF] Li | Ontology-based semantic similarity in generating context-aware collaborator recommendations[END_REF]:

5 S(d, c) = I i=1 S i 1 (d, c) + J j=1 S j 2 (d, c) (3)
where I represents the number of dimensions that contain qualitative objects; J represents the number of dimensions that contain quantitative objects; Based on the semantic similarity S(d, c) and two context-aware recommendation approaches (i.e., PreF and PoF), three context-aware collaborator recommendation algorithms can be developed: PreF1, PoF1, and PoF2. Particularly, PreF1 and PoF2 are already explained in [START_REF] Li | Ontology-based semantic similarity in generating context-aware collaborator recommendations[END_REF]. Thus, this paper only introduces PoF1 algorithm (see Algorithm 1) and differences among the three algorithms (see Fig. 2). It first utilizes a technique of 2D recommendation approaches to predict users' unknown ratings for collaborators (line 1-3). Then, it computes ontology-based semantic similarities between the collaboration c and other collaborations d (d ∈ X, d = c), and a sum of semantic similarities between the collaboration c and the recent K collaborations that collaborator i (i = u) participated (line 6-13). Next, users' adjusted ratings for collaborators are computed according to predicted ratings, calculated semantic similarities, and their weights w s , w r (line 4-5, 14-21). Finally, the top K collaborators with higher adjusted ratings will be recommended to the user u (line 22).

I + J = T ,
PreF1 [START_REF] Li | Ontology-based semantic similarity in generating context-aware collaborator recommendations[END_REF] first pre-processes the collaboration context by means of semantic similarity, then generates 2D collaborator recommendations, and finally produce context-aware collaborator recommendations (see Fig. 2). As for PoF1 (see Algorithm 1) and PoF2 [START_REF] Li | Ontology-based semantic similarity in generating context-aware collaborator recommendations[END_REF], they generate 2D collaborator recommendations, then process the collaboration context using semantic similarity, and eventually produce context-aware collaborator recommendations (see Fig. 2). The differences between PoF1 and PoF2 are on how to apply semantic similarity in filtering or adjusting the the order of collaborators i (i = u, i / ∈ O c,Col ). 5 The detailed equations of S i 1 (d, c) and S j 2 (d, c) are available in [START_REF] Li | Ontology-based semantic similarity in generating context-aware collaborator recommendations[END_REF]. This paper do not discuss how to calculate S i 1 (d, c) and S j 2 (d, c).

Algorithm 1: PoF1 algorithm.

Input: The rating matrix: R, the user: u, the collaboration: c, the set of members in the collaboration c: O c Col , the number of recommendations: K, the number of known collaborations: |X|, the number of users: m, the weight of semantic similarity in adjusted ratings: ws, the weight of predicted rating in adjusted ratings: wr, the number of dimensions that contain qualitative objects: I, the number of dimensions that contain quantitative objects: J. Initialize: Two lists with zeros: SC (of length |X|) and V U (of length m).

if k / ∈ O c,Col then 20 if V U (k) == 1 then 21 R(k) ← ws * sum(SC(k)) + wr * R uk ;
22 Rank R in decreasing order and get K highest ratings; Output: User u's adjusted ratings R, K collaborators with K highest ratings. Using the three algorithms (i.e., PreF1, PoF1, and PoF2), context-aware collaborator recommendations can be produced for users. Specifically, all these algorithms can employ the same technique of 2D recommendation approaches and our proposed ontology-based semantic similarity [START_REF] Li | Ontology-based semantic similarity in generating context-aware collaborator recommendations[END_REF], which makes it possible to test, compare, and analyze their performances through experiments.

Experiments

Dataset & Evaluation methods To test and evaluate the performances of PreF1, PoF1, and PoF2, we apply an academic publication dataset6 [START_REF] Tang | Arnetminer: Extraction and mining of academic social networks[END_REF]. It includes academic articles and their citation relationships until 2019-05-05, which are extracted from DBLP, MAG, and AMiner. All these articles are organized in a non-mutually exclusive hierarchy with 20 top-level domains 7 . This allows us to separate the dataset into 20 blocks. Each block contain articles in a top-level domain.

Particularly, each article in a block represents the fact that its authors have collaborated once in a top-level domain. During such a collaboration, the authors work together to write the corresponding article. This implies that an academic article can be considered as a scientific collaboration. Thus, the side information of an article belongs to the context of a scientific collaboration. Accordingly, each block of articles can be considered as a set of scientific collaborations with their contexts in the corresponding top-level domain.

Specifically, every set is composed of 1000 articles selected randomly from a block due to the different article numbers in these blocks. These articles are arbitrarily divided into two parts, representing separately training collaboration and testing collaborations. Particularly in the three context-aware collaborator recommendation algorithms (i.e., PreF1, PoF1, and PoF2), training collaborations constitute the set X, providing known information (e.g., known ratings). Meanwhile, each testing collaboration is c. For every author u in a testing collaboration c, context-aware collaborator recommendations are generated and analyzed in our experiments.

Particularly, for all scientific collaborations, we have T = 7, I = 1, and J = 6. Therefore, based on Eq. 3, the ontology-based semantic similarity between two scientific collaborations (c and d) 8 is:

S(d, c) = S 1 (d, c) + 6 j=1 S j 2 (d, c) (4)
Within this semantic similarity S(d, c), we can conduct experiments to analyze the performances of PreF1, PoF1, and PoF2 in terms of accuracy and time efficiency. To this end, we employ three metrics: F1 [START_REF] Goutte | A probabilistic interpretation of precision, recall and f-score, with implication for evaluation[END_REF], Mean Absolute Error (MAE) [START_REF] Willmott | Advantages of the mean absolute error (mae) over the root mean square error (rmse) in assessing average model performance[END_REF], and execution time. Particularly, a higher value of F19 and/or a lower value of MAE10 indicates more accurate recommendations. As for time efficiency, we measure the execution time 11 that each algorithm takes to generate context-aware collaborator recommendations for an author u in a testing collaboration c. Lower execution time represents higher time efficiency.

With the three metrics (i.e., F1, MAE, and execution time), two types of experiments are carried out: experiment with different semantic similarities and experiment with different 2D recommendation techniques.

Experiment with different semantic similarities In this experiment, we change the semantic similarity applied in PreF1, PoF1, and PoF2. This provides us an opportunity to investigate how much our semantic similarity [START_REF] Li | Ontology-based semantic similarity in generating context-aware collaborator recommendations[END_REF] contributes to generating context-aware collaborator recommendations. Particularly, our semantic similarity is inspired and developed by other types of semantic similarities [START_REF] Li | Ontology-based semantic similarity in generating context-aware collaborator recommendations[END_REF]. Thus, we need to utilize existing semantic similarities of these types in PreF1, PoF1, and PoF2. Specifically, our experiments involves 5 existing semantic similarities, including Jaccard, Dice, Tversky, TF-IDF, and IC12 [START_REF] Sánchez | Ontology-based semantic similarity: A new feature-based approach[END_REF].

Each experiment uses a different semantic similarity in a set of scientific collaborations. To analyze their performances in the algorithms, F1, MAE and execution time are employed. All the results are shown in Fig. 3, 4, and5. In Fig. 3, our semantic similarity leads to the highest value of F1 when applied in PoF1 and PoF2. This indicates that our semantic similarity can enhance F1 and thus generate more accurate context-aware collaborator recommendations. But it only achieve a medium value of F1 in PreF1. These varied values of F1 imply that the enhancing effect of our semantic similarity depends on the recommendation algorithms, which is driven by the different processing steps of semantic similarities in the algorithms (see Fig. 2).

Besides, when employing our semantic similarity in the algorithms, their MAE results are always lower than those of Jaccard, Tversky, and IC. However, compared to Dice and TF-IDF, our semantic similarity produces slightly higher MAE results (except TF-IDF in PoF1). Considering that our semantic similarity brings significantly better results than Dice and TF-IDF in terms of F1, it is fair to conclude that our ontology-based semantic similarity can improve the accuracy of PoF1 and PoF2. When implemented in PreF1, our ontology-based semantic similarity has an average performance of accuracy, which is acceptable. Lastly, our semantic similarity evidently achieves the shortest execution time among all semantic similarities. This indicates that the time efficiencies of PreF1, PoF1, and PoF2 are augmented through the use of our semantic similarity.

Experiment with different 2D recommendation techniques In this experiment, we employ two 2D recommendation techniques in the three contextaware collaborator recommendation algorithms: Neural network-based Collaborative Filtering (NCF) [START_REF] He | Neural collaborative filtering[END_REF] and Probabilistic Matrix Factorization (PMF) [START_REF] Mnih | Probabilistic matrix factorization[END_REF]. Both techniques belongs to CF approach (cf. Section 2.1). Applying the two techniques in PreF1, PoF1, and PoF2 gives us a chance to explore whether applying our semantic similarity with different 2D recommendation techniques can influence the performances of the three algorithms. Similarly, the accuracy and time efficiency are also evaluated through the three metrics: F1, MAE and execution time. All the results are shown in Fig. 6, 7, and 8.

In summary, when either PMF or NCF is applied in PreF1, PoF2 and PoF1, all values of F1 are higher than those of PMF and NCF themselves (represented as NCF/PMF in Fig. 6, 7, and8). This indicates that our semantic similarity can increase F1 of PreF1, PoF2 and PoF1 whatever 2D recommendation technique is used. However, F1 values with NCF are much higher than those with PMF. This implies that the enhancement of F1 driven by our semantic similarity relates to the techniques used to generate 2D collaborator recommendations. Between NCF and PMF, our semantic similarity can attain greater F1 with NCF.

Meanwhile, compared with NCF/PMF, lower MAE are also reached when applying PMF and NCF in PreF1, PoF2 and PoF1 (except PMF in PoF1). This signifies that our semantic similarity, while using either PMF or NCF in the algorithms, can reduce values of MAE. Similarly, the decreased MAE values with NCF are larger than those with PMF. This also means that the reduction of MAE is caused by our semantic similarity but linked to the techniques used to generate 2D collaborator recommendations. Both higher F1 and lower MAE suggest that our semantic similarity improves the accuracy of PreF1, PoF2, and PoF1. Only its enhancements are more evident with NCF than with PMF.

As for execution time, the results of PoF2, PoF1, and NCF/PMF are very near. On the contrary, the execution time of PreF1 is much longer than those of other algorithms, indicating a higher time complexity of PreF1.

Discussion

Utilizing a dataset of scientific collaborations, we conduct two types of experiments to analyze the performance of three context-aware collaborator recommendations algorithms (i.e., PreF1, PoF1, and PoF2) from two aspects: accuracy and time efficiency. Based on the results, the following can be concluded:

-Our ontology-based semantic similarity [START_REF] Li | Ontology-based semantic similarity in generating context-aware collaborator recommendations[END_REF] The above summary signifies that with our ontology-based semantic similarity, PreF1, PoF1, and PoF2 algorithms can enhance their performances, either in terms of accuracy or time efficiency, or both. The differences in improvement may be caused by the order of processing our semantic similarity in the algorithms, which deserves further investigation.

Besides, our ontology-based semantic similarity enables us to deal with the collaboration context in the context-aware collaborator recommendation generation processes. This type of context is never considered or discussed in previous studies on such recommendations. These previous studies usually focus on either user context (e.g., [START_REF] Liu | Context-aware academic collaborator recommendation[END_REF]) or item context (e.g., [START_REF] Xu | A personalized researcher recommendation approach in academic contexts: Combining social networks and semantic concepts analysis[END_REF]). None of the previous studies takes into account users and items together. With the collaboration context, users and items are considered jointly in collaborations. This deepens the comprehension of both users and items in context-aware collaborator recommendations.

Also, this work has some limitations. The recommendations produced by PreF1 and PoF2 [START_REF] Li | Ontology-based semantic similarity in generating context-aware collaborator recommendations[END_REF] may have a serendipity problem [START_REF] De Gemmis | An investigation on the serendipity problem in recommender systems[END_REF]: the recommended collaborators are not 'surprising' to users. This leads to insufficient diversity of recommendations: it is often the same collaborators that are recommended to users. Based on PreF1 and PoF2 [START_REF] Li | Ontology-based semantic similarity in generating context-aware collaborator recommendations[END_REF], each collaborator recommended to the user must have involved in collaborations with high similarities. Such collaborators are obvious to facilitate users' collaborations, but not the good ones. The collaborators have not involved in the same collaborations with the user should also be included, which may result in surprising and diverse recommendations.

Conclusion & Future Work

In this paper, we focus on how to analyze the performances of three contextaware collaborator recommendation algorithms. To solve this issue, two types of experiments are effected in a dataset of scientific collaborations and analyzed in terms of accuracy and time efficiency.

Based on the literature review, we decided to follow PreF and PoF approaches for developing three corresponding context-aware collaborator algorithms: PreF1, PoF1, and PoF2. We then presented how the three algorithms can be used to generate context-aware collaborator recommendations based on a collaboration context ontology and an ontology-based semantic similarity. Finally, a public dataset of scientific collaborations was applied in two types of experiments to test and analyze the performances of the three algorithms through three metrics (i.e., F1, mean absolute error and execution time). The first two metrics serve to evaluate the accuracy of the three algorithms, while the last one aims to measure the time efficiency.

Our future work is to improve and enrich the experiments of the three algorithms. This may helps us to ananlyze why applying a same semantic similarity in the algorithms can result in different improvements.

Fig. 1 .

 1 Fig. 1. Main steps of PreF, PoF, and CM [3].

D 1 ,

 1 D 2 , and 2D recommendation techniques to predict unknown ratings and thus generate context-aware recommendations for users. -Contextual post-filtering (PoF) approach starts with D 1 , D 2 , and 2D recommendation techniques, producing 2D recommendations. Afterwards, we utilize D 3 , ..., D n to filter out the irrelevant 2D recommendation results or adjust their orders and thus generate context-aware recommendations [3].

  T represents the maximum number of dimensions that the context of the collaboration c can contain. Besides, S(d, c) ∈ [0, 1]. SmallerS(d, c) implies greater difference between c and d.

Fig. 2 .

 2 Fig. 2. Main steps in PreF1, PoF1, and PoF2.

Fig. 3 .

 3 Fig. 3. F1 with different semantic similarities in a set of scientific collaborations.

Fig. 4 .

 4 Fig. 4. MAE with different semantic similarities in a set of scientific collaborations.

Fig. 5 .

 5 Fig. 5. Execution time with different semantic similarities in a set of scientific collaborations.

Fig. 6 .

 6 Fig. 6. F1 with different 2D recommendation techniques in a set of scientific collaborations.

Fig. 7 .

 7 Fig. 7. MAE with different 2D recommendation techniques in a set of scientific collaborations.

Fig. 8 .

 8 Fig. 8. Execution time with different 2D recommendation techniques in a set of scientific collaborations.

  1 for h ∈ {1, 2, .., m} AND k ∈ {1, 2, .., m} do

	2	if R hk is unknown then
	3	apply techniques of 2D recommendation approaches to predict
		unknown ratings R hk ;
	8	S(d, c) ← 0 ;
	9	else
	10	S(d, c) ← I i=1 S i 1 (d, c) + J j=1 S j 2 (d, c);

4 if h == u then 5 V U (k) ← 1; 6 for d ∈ {1, 2, .., |X|} do 7 if d == c then

11 while i ∈ O c,Col do 12 if collaboration y belongs to collaborator i's rencent K collaborations then 13 SC(i).insert(S(d, c)); 14 for k ∈ {1, 2, .., m} do 15 for d ∈ {1, 2, .., length(SC)} do 16 if k / ∈ O c,Col then 17 V U (k) ← 1; 18 for k ∈ {1, 2, .., m} do 19

  can lead to better time efficiency of PreF1, PoF1, and PoF2. It also leads to higher accuracy in PoF1 and PoF2, but shows no improvement of accuracy in PreF1. -Calculating our ontology-based semantic similarity in PreF1, PoF1, and PoF2 can produce more accurate context-aware collaborator recommendations, regardless of the applied 2D recommendation technique. However, it positive effect on time efficiency isn't very obvious.

Such a RS is also mentioned as 2D RS in the rest of this paper.

Fig. 1 also illustrates how D1, D2, ..., Dn are utilized in different methods.

This dataset can downloaded from https://www.aminer.org/citation.

These domains are Art, Biology, Business, Chemistry, Computer science, Economics, Engineering, Environmental science, Geography, Geology, History, Materials science, Mathematics, Medicine, Philosophy, Physics, Political science, Psychology, Sociology, and Others.

Here, c is a testing collaboration; |X| represents the number of training collaborations; d(d ∈ X, d = c) is a training collaboration.

[START_REF] He | Neural collaborative filtering[END_REF] The range of F1 is [0, 1

].[START_REF] Jin | An automatic weighting scheme for collaborative filtering[END_REF] The range of MAE is [0,

+∞).[START_REF] Koren | Advances in collaborative filtering[END_REF] In our experiments, execution time is counted in

milliseconds.[START_REF] Li | Towards a collaboration context ontology[END_REF] Here, IC represents IC(c) = -log p(c), where p(c) is the probability of c's appearance in an ontology[START_REF] Sánchez | Ontology-based semantic similarity: A new feature-based approach[END_REF].


Siying Li
email: siying.li@utc.fr

Marie-Hélène Abel
email: marie-helene.abel@utc.fr

Elsa Negre
email: elsa.negre@lamsade.dauphine.fr

Keywords: Ontology-based semantic similarity, Context-aware recommendations, Collaborator, Collaboration context

Nowadays, the number of collaborative tools has increased significantly. This makes it difficult for users to find the collaborators that are most relevant to their needs among these tools. Besides, their needs can also be influenced by the context of collaboration (e.g., workplace, tools, and resources). This raises an issue: how to help users find their collaborators within the collaboration context. In our research, we propose an ontologybased semantic similarity and employ it in a collaboration context ontology to generate context-aware collaborator recommendations for users. In this paper, we present how to calculate and apply the semantic similarity in context-aware recommendation algorithms.

I. INTRODUCTION

With the advancement of information technology, collaborative tools have been rapidly developed (e.g. instant messaging and resource management tools), leading to a significant increase in their amount. This offers users with convenience during collaborations [START_REF] Patel | Factors of collaborative working: A framework for a collaboration model[END_REF] [START_REF] Mattessich | Collaboration: what makes it work. A review of research literature on factors influencing successful collaboration[END_REF]. However, it also causes difficulties for users in finding the most relevant collaborators to their needs among these tools [START_REF] Wang | Sustainable collaborator recommendation based on conference closure[END_REF] [START_REF] Yang | A nearest neighbor based personal rank algorithm for collaborator recommendation[END_REF]. Besides, due to the pandemic, users collaborate remotely under different contexts (e.g., workplace, tools, and resources) affecting users' needs during collaborations. This requires us to take the context of the collaboration into account when searching for collaborators. Therefore, one of the current issues is how to help users find their collaborators within the collaboration context.

To bridge the gap, collaborator recommendations are generated and intended to aid users in seeking out and choosing collaborators [START_REF] Wang | Sustainable collaborator recommendation based on conference closure[END_REF] [START_REF] Yang | Scientific collaborator recommendation in heterogeneous bibliographic networks[END_REF]. However, due to the missing consideration of the context, these recommendations are sometimes not consistent with users' needs. Thus, we intend to incorporate the collaboration context into recommendation generation processes for producing more relevant recommendations, contextaware collaborator recommendations [START_REF] Adomavicius | Context-aware recommender systems[END_REF]. Among the different methods of generating such recommendations [START_REF] Adomavicius | Context-aware recommender systems[END_REF], we decide to employ contextual pre-filtering and post-filtering due to their advantages in terms of cost and computational complexity.

Specifically, the collaboration context is defined in an ontology, where all information is specified through semantic 3-uples <Subject, Predicate, Object> [START_REF] Li | Towards a collaboration context ontology[END_REF] [START_REF] Siying | Managing and recommending resources in web-based collaborative working environments[END_REF]. While dealing with such information, ontology-based semantic similarities can be applied [START_REF] Zhang | Semantic similarity between ontologies at different scales[END_REF]- [START_REF] Zhao | A novel method on information recommendation via hybrid similarity[END_REF]. It allows us to measure the closeness between two collections of semantic 3-uples, which represent two collaborations and their contexts. Hence, we develop and utilize a new ontology-based semantic similarity to process information in the collaboration context ontology and thus generate context-aware collaborator recommendations for users.

The remainder of this paper is constructed as follows. Section II studies context-aware recommendations and ontology-based semantic similarities. Section III presents our contributions in (i) developing a new ontology-based semantic similarity, (ii) calculating it in a collaboration context ontology, (iii) employing it in two methods to generate context-aware collaborator recommendations for users. We then discuss the strengths and weaknesses of the ontology-based semantic similarity in Section IV. Finally, some conclusions and future work are shown in Section V.

II. RELATED WORK

This section introduces what are context-aware recommendations and how they can be generated. We also investigate existing ontology-based semantic similarities and analyze their characteristics.

A. Context-aware recommendations

When generating recommendations for users, two dimensions of data are usually applied: users and items1 [START_REF] Adomavicius | Incorporating contextual information in recommender systems using a multidimensional approach[END_REF]. Here, items are objects that are recommended to users [START_REF] Ricci | Introduction to recommender systems handbook[END_REF]. In 2D collaborator recommendations, a collaborator is an item. These items are sorted by their ratings, indicating how a particular user liked a specific item [START_REF] Ricci | Introduction to recommender systems handbook[END_REF].

While producing context-aware recommendations for users, the context is incorporated into recommendation generation processes [START_REF] Adomavicius | Context-aware recommender systems[END_REF]. Such recommendations are generated by dealing with at least three dimensions of data: User, Item and Context 2 . Sometimes, it can even handle multi-dimensions. For example, [START_REF] Adomavicius | Incorporating contextual information in recommender systems using a multidimensional approach[END_REF] utilized 5 dimensions: User, Item, Place, Time and Companion for context-aware movie recommendations. Thus, with n-dimensional data and an initial set of ratings, users' unknown ratings for items can be predicted by (1) [START_REF] Adomavicius | Incorporating contextual information in recommender systems using a multidimensional approach[END_REF]:

R : D 1 × D 2 × ... × D n → Rating(n ≥ 3, n ∈ N * ) (1)
where D 1 , D 2 , ..., D n represent the n dimensions of data: D 1 = U ser; D 2 = Item; D 3 ..., D n = Context (e.g., place, time).

Particularly, [START_REF] Adomavicius | Context-aware recommender systems[END_REF] proposed three methods to incorporate the context in different phases of recommendation processes (see Fig. 1) 3 , as follows:

• Contextual pre-filtering (PreF) starts by applying D 3 , ..., D n to filter ratings that are irrelevant to specific contexts [START_REF] Adomavicius | Incorporating contextual information in recommender systems using a multidimensional approach[END_REF]. Afterwards, D 1 , D 2 , and approaches of 2D recommendations are used to predict unknown ratings and thus generate context-aware recommendations for users. Among these methods, CM is too costly when data volume and complexity are heavy. It can not handle the same amount of users and items as other methods (i.e., PreF and PoF). In each phase of the recommendation generation process, CM needs to process n dimensions of data, whereas PreF and PoF only focus on partial dimensions (either D 1 ×D 2 or D 3 ×...×D n ). Besides, as n increases, the computational complexity of CM becomes higher. However, for PreF and PoF, only the phase of processing D 3 ... × D n becomes complicated. Thus, we concentrate on applying PreF and PoF to generate context-aware collaborator recommendations for users.

B. Ontology-based semantic similarity

An ontology is a formal and explicit specification of a shared, agreed and detailed conceptualization [START_REF] Peckham | Semantic data models[END_REF] [START_REF] Du | Apports des ontologies aux systèmes de recommandation : état de l'art et perspectives[END_REF]. It applies semantic 3-uples <Subject, Predicate, Object> to describe and represent information. In ontologies, the closeness between two terms 4 is computed by ontology-based semantic similarities, which can be classified into different types based on the information contained in terms and/or the calculation method.

First, three types of semantic similarities are summarized, depending on the information contained in terms [START_REF] Sánchez | Ontology-based semantic similarity: A new feature-based approach[END_REF]- [START_REF] Zhao | A novel method on information recommendation via hybrid similarity[END_REF]: 1) Path-based similarities are calculated based on the shortest path between two terms [START_REF] Zhang | Medical document clustering using ontology-based term similarity measures[END_REF]. The longer the shortest path, the more semantically different the two terms are [START_REF] Sánchez | Ontology-based semantic similarity: A new feature-based approach[END_REF]; 2) Feature-based similarities consider an term as a set of ontological features [13] [14]. The more common features and the less non-common features two terms have, the more similar they are [START_REF] Varelas | Semantic similarity methods in wordnet and their application to information retrieval on the web[END_REF]. To compare features, several coefficients on the sets are applicable, such as Jaccard index

J(O x , O y ) = |O x ∩O y | |O x |+|O y |-|O x ∩O y | 5 [22], Dice coefficient D(O x , O y ) = 2|O x ∩O y | |O x |+|O y | 6 [23], and Tversky index T (O x , O y ) = |O x ∩O y | |O x ∩O y |+α|O x -O y |+β|O y -O x |
7 [START_REF] Tversky | Features of similarity[END_REF]; 3) Information content-based similarities measure the amount of information provided by a common ancestor of two temrs in an ontology [13] [14]. Particularly for a term x, IC(x) = -log p(x))8 is utilized to identify the amount of x's provided information.

Particularly, when the compared terms are collections of semantic 3-uples, semantic similarities can be divided into pairwise and groupwise similarities, based on the calculation method [START_REF] Zhang | Semantic similarity between ontologies at different scales[END_REF]. Pairwise similarity is a combination of similarities between individual subjects, predicates, or objects in the two collections, which can consider either every pair or only the best-matching pair [START_REF] Pesquita | Semantic similarity in biomedical ontologies[END_REF]. Secondly, groupwise similarities are directly calculate by one of three collection presentations: set, graph, or vector, such as the similarities between two graphs [START_REF] Zhang | Semantic similarity between ontologies at different scales[END_REF]- [START_REF] Wang | Measurement and computation of profile similarity of workflow nets based on behavioral relation matrix[END_REF].

These ontology-based semantic similarities have their own advantages and disadvantages. For example, path-based similarities do not necessitate the detailed information of each term, which is an advantage. However, they have a strong dependence on the degree of completeness and coverage of predicates in an ontology [START_REF] Cimiano | Ontology Learning and Population from Text -Algorithms[END_REF]. As for feature-based similarities, they can be employed in cross ontologies (i.e. when the two terms belong to different ontologies) [START_REF] Petrakis | Xsimilarity: Computing semantic similarity between concepts from different ontologies[END_REF], but require detailed information about the features of each term. Besides, using information content-based similarities, infrequent terms are more informative than the frequent ones [START_REF] Sánchez | Ontology-based semantic similarity: A new feature-based approach[END_REF]. But they request the recursive computation of all subjects', objects' and predicates' appearances in an ontology. If any subject, object, or predicate changes, recalculations are mandatory. Pairwise similarities can apply all the first types of similarities (i.e., path-based, featurebased, and information content-based similarities) for each pair, while groupwise similarities are limited due to the collection presentation.

Nevertheless, a common disadvantage is that they utilize only partial information in ontologies. For instance, path-based similarities employ information related to the shortest path, while feature-based similarities only focus on features of each term. This makes it hard to compare two terms with all their detailed information. Therefore, inspired by feature-based, information content-based, and groupwise similarities, a new ontology-based semantic similarity is built and employed in our research. It can not only compare the common and noncommon features of subjects (objects) in two collections of semantic 3-uples, but also assess the amount of information provided by different involved predicates.

III. CONTRIBUTIONS

This section explains how to generate context-aware collaborator recommendations by computing an ontology-based semantic similarity in a collaboration context ontology and implementing it in two methods (i.e., PreF and PoF). In doing so, two corresponding context-aware recommendation algorithms are constructed, separately following PreF and PoF. Finally, these algorithms are presented.

A. A collaboration context ontology

The collaboration context ontology MEMORAe-Collaboration-Context (MCC) [START_REF] Li | Towards a collaboration context ontology[END_REF] employs a subject and its involved semantic 3-uples to define the collaboration context. Specifically, the subject itself indicates a collaboration. Surrounding it, eight dimensions of the collaboration context are represented by different predicates and objects, including: Goal, Collaborator, Activity, Resource, Time, Location, Relation, and Satisfaction [START_REF] Li | Towards a collaboration context ontology[END_REF]. Thus, a collaboration c and its context are formulated as a collection of semantic 3-uples in MCC: < c, p c,t g , o c,t g > |g ≤ G c , t ≤ T, g, t ∈ N + . Here, p c,t g is a predicate that the collaboration c contains, belonging to the t th dimension; P c,t (= p c,t g ) is a set of predicates that the collaboration c contains in the t th dimension; P c (= p c g ) is the set of all predicates that the collaboration

c contains; o c,t g (∈ O c,t ) is an object of the predicate p c,t g ; O c,t (= o c,t g
) is a set of objects that the collaboration c contains through predicates in P c,t ; O c (= o c g ) is the set of all objects that the collaboration c contains through predicates in P c ; G c is the number of predicates that the collaboration c contains; T represents the maximum number of dimensions that the collaboration c can contain.

Within such collections of semantic 3-uples in MCC, we are able not only to compare the common and non-common objects in two collections, but also to assess the amount of information provided by a specific predicate in two collections. Thus, we develop a new groupwise semantic similarity to measure the closeness between two collections of semantic 3-uples.

B. An ontology-based semantic similarity

The ontology-based groupwise semantic similarity aims to compare two collections of semantic 3-uples <Subject, Predicate, Object>, which respectively stand for two collaborations (represented by two subjects c and d) and their contexts. Inspired by the existing ontology-based semantic similarities (cf. Section II-B), it is calculated from two aspects: Object (built on feature-based semantic similarities) and Predicate (built on information content-based semantic similarities).

a) Object: This aspect measures the common and noncommon objects that are related to the same predicates in two collections of semantic 3-uples. Particularly, both qualitative and quantitative objects are considered.

Qualitative objects contain non-numerical and descriptive information. For example, when comparing whether the two collections include the same collaborators, the collaborators are qualitative objects. These objects can be associated with different predicates in the two collections. When they are linked to a same predicate p i g (i = 1, 2, ..., T ), they constitute separately two sets of objects: O c p i g and O d p i g , which are measured by (2) 9 .

S i 1 (c, d) = |P cd,i | g=1 |O c p i g ∩ O d p i g | × IC(P c,i ) T t=1 IC(P c,t ) |O c p i g ∩ O d p i g | + α|O c p i g -O d p i g | + β|O d p i g -O c p i g | (2)
where p i g is a predicate that both c and d contain, belonging to the i th dimension; O d | denotes the absolute differences between two 9 The range of S cd,i 1 is [0,

IC(P c,i ) 8
t=1 IC(P c,t ) ]. 10 The calculation of IC(P c,i ) will be presented later. 11 Here,

IC(P c,i ) T t=1 IC(P c,t )
serves to normalize values of S cd,i 1 . 12 The range of S j 2 (c, d) is [0,

IC(P c,j ) T t=1 IC(P c,t )
].

13 Equation ( 3 qualitative objects that c and d contains through the predicate p j g . Notably, (3) is only suitable for o p j g whose range of is [0, +∞). Particularly, if the range of o p j g is [0, L] 14 , then (3) is transformed into:

S j 2 (c, d) = |P cd,j | g=1 ( L+1 L |o c p j g -o d p j g | + 1 - 1 L )× IC(P c,j ) T t=1 IC(P c,t ) (4)
b) Predicate: This aspect computes the amount of information provided by a specific predicate, reflecting the importance of this predicate. Particularly, the appearance frequency and contribution of a predicate in one collection of semantic 3-uples matter in this computation. Thus, we decide to employ TF-IDF [START_REF] Rajaraman | Mining of massive datasets[END_REF]. Specifically, we replace "term, document, and corpus" in TF-IDF as following for "predicate (factor), a collaboration, and a collection of collaborations" (see Fig. 2). For a predicate p in a collaboration c (c ∈ X, X represents a set of collaborations) and the total number of collaborations in the set is |X|, we have 15

tf (p, c) = f (p,P c ) p ∈P c f (p ,P c ) idf (p, X) = log |X| 1+|c∈X:p∈P c | + 1 tf • idf (p, c, X) = tf (p, c) • idf (p, X) (5)
where f (p, P c ) represents the appearance frequency of the predicate p in c;

p ∈P c f (p , P c ) denotes the appearance frequencies of all predicates in c.

Then the amount of information provided by the predicate p in the collaboration c is IC(p) = tf • idf (p, c, X). As for the amount of information provided by the predicates belonging to the t th dimension: IC(P c,t )(t = 1, 2, ..., T ), it is calculated through (6) 16 :

IC(P c,t ) = |P c,t | q=1 tf • idf (p c,t q , c, X) (6)
where |P c,t | is the number of predicates that the collaboration c contains, belonging to the t th dimension; p c,t q ∈ P c,t . 14 Here, L represents the maximum value in the range of o p j g . 15 Particularly, the range of tf (p, c) is [0, 1] and the range of idf (p, X)

is [log |X| 1+|X| + 1, log|X| + 1]. Thus, the range of tf • idf (p, c, X) is [0, log|X| + 1]
. 16 The range of

IC(P c,t ) is [0, 2(log|X| + 1)].
c) Calculation: Combining eq. ( 2), 3, and 4, the semantic similarity S(c, d) between c and d can be computed as follows. Its range is [0, 1].

S(c, d)

= I i=1 S i 1 (c, d) + J j=1 S j 2 (c, d) (7)
where I represents the number of dimensions that contain qualitative objects; J represents the number of dimensions that contain quantitative objects; I + J = T . In MCC, we have T = 8, I = 6 (i.e., Goal, Collaborator, Activity, Resource, Location, and Relation) and J = 2 (i.e., Time and Satisfaction) [START_REF] Li | Towards a collaboration context ontology[END_REF]. Thus, the ontology-based semantic similarity S(c, d) in MCC is calculated as shown in ( 8) 17 .

S(c, d) = 6 i=1 S i 1 (c, d) + 2 j=1 S j 2 (c, d) (8)
Particularly,

if k ∈ O d Col then 16 V U (k) ← 1; 17 for k ∈ {1, 2, .., m} do 18 R uk ← R uk × V U (k)
19 Rank R u * in decreasing order and get K highest ratings; Output: User u's ratings R u * , K collaborators with K highest ratings.

In Algorithm 2, we first employ approaches of 2D recommendations to predict users' unknown ratings for collaborators (line 1-5). Then, it computes ontology-based semantic similarities between the collaboration c and other collaborations d (d ∈ X, d = c), and find similar collaborations with the K highest semantic similarity (line 6-12). Next, irrelevant collaborators v that did not participate in these similar collaborators are filtered out (line [START_REF] Sánchez | Ontology-based semantic similarity: A new feature-based approach[END_REF][START_REF] Zhang | Medical document clustering using ontology-based term similarity measures[END_REF][START_REF] Zhao | A novel method on information recommendation via hybrid similarity[END_REF][START_REF] Adomavicius | Incorporating contextual information in recommender systems using a multidimensional approach[END_REF][START_REF] Ricci | Introduction to recommender systems handbook[END_REF][START_REF] Dey | Understanding and using context[END_REF]. Finally, the top K collaborators with higher ratings will be recommended to the user u (line 19). To summarize, Algorithm 2 starts by applying approaches of 2D recommendations, then calculates the ontology-based semantic similarity, and eventually generates context-aware collaborator recommendations for users.

Using the above algorithms of PreF and PoF methods (Algorithms 1 and 2), context-aware collaborator recommendations can be generated for users. Particularly, both PreF and PoF methods employ the ontology-based semantic similarities in the recommendation generating processes, but in different orders.

IV. DISCUSSION

The new ontology-based semantic similarity, which is calculated by [START_REF] Li | Towards a collaboration context ontology[END_REF], measures the closeness between two collections of semantic 3-uples representing two collaborations and their contexts. This semantic similarity not only measures the objects but also considers the importance of their related predicates, which are reflected by the amount of information provided by these predicates.

Besides, applying this semantic similarity in PreF and PoF methods permit us to generate more accurate collaborator recommendations, context-aware collaborator recommendations 19 . This also enables us to identify users' ratings for collaborators within the whole context of collaboration, instead of the partial context of user or item (collaborator). For instance, [START_REF] Al Jawarneh | A pre-filtering approach for incorporating contextual information into deep learning based recommender systems[END_REF] only took into account some of item context in their algorithm following PreF method. Furthermore, since both users and items belong to a collaboration, our algorithms collectively consider users and items within the collaboration context, rather than considering separately the context of user or item.

V. CONCLUSION AND FUTURE WORK

In this paper, we focus on how to recommend collaborators for users within the collaboration context. To solve this issue, we develop a new ontology-based semantic similarity, calculate it in a collaboration context ontology, and utilize it in two context-aware collaborator recommendation algorithms. Based on the literature review, we explain context-aware recommendations and compare existing ontology-based semantic similarities. We also investigate how to compute the new ontologybased semantic similarity in a collaboration context ontology and employ it in two algorithms to generate context-aware collaborator recommendations. Our future work is to finalize and improve the experiments about the two algorithms.

Fig. 1 .

 1 Fig. 1. Main phases of PreF, PoF, and CM [6].

3

  Fig. 1 also illustrates how D 1 , D 2 , ..., Dn are utilized in different methods.

|

  of qualitative objects that d relates through the predicate p i g ; represents the number of common objects associated to c and d through the predicate p i g ; |P cd,i | represents the number of predicates belonging to the i th dimension that both c and d contain; IC(P c,i ) expresses the amount of information provided by the predicates that c contains, belonging to the i th dimension 10 ; T t=1 IC(P c,t ) is the sum amount of information provided by the predicates that c contains 11 ; α, β(≥ 0) indicates the weights of c and d. The smaller the semantic similarity S i 1 (c, d) is, the more differences there are between c and d in the i th dimension of the collaboration context.Quantitative objects include numerical information, such as start time and end time of a collaboration[START_REF] Li | Towards a collaboration context ontology[END_REF]. To compare two such objects, the absolute difference |o c = 1, 2, ..., T ) is utilized. The smaller the absolute difference is, the greater the similarity between o

  ) intends to convert |o c p j g -o d p j g |, which is inspired from(2) and the discussion on the site https://stats.stackexchange.com/questions/ 158279/how-i-can-convert-distance-euclidean-to-similarity-score.

Fig. 2 .

 2 Fig. 2. Apply TF-IDF to measure the amount of information provided by predicates.

  c,T i ) 8 t=1 IC(P c,t ) + ( L Sa +1 L Sa |o c p Sa -o d p Sa |+1 -1 L Sa ) × IC(P c,Sa ) 8 t=1 IC(P c,t ) , where L Sa is the maximum value in the range of individuals' satisfactions to collaborations 18 ; o c p Sa denotes the average of all given satisfactions to the collaboration c. Within this ontology-based semantic similarity S(c, d), the closeness between two collections of semantic 3-uples can be measured. Each collection contains information relevant to a collaboration and its context. Therefore, through S(c, d), the collaboration context in MCC can be processed to generate context-aware collaborator recommendations for users. C. Context-aware collaborator recommendation algorithms Within the ontology-based semantic similarity S(c, d) in MCC, the context-aware collaborator recommendation problem is formulated as: Given a rating matrix R and a user u in a collaboration c (u ∈ O c,Col ), the top K collaborators v (v = u, v / ∈ O c,Col ) that can facilitate u's collaboration c with the highest probabilities will be recommended to u. Here, the context indicates the context of u's collaboration c, which is represented by a collection of semantic 3-uples < c, p c,t g , o c,t g > |g ≤ G c , t ≤ 8, g, t ∈ N + . To address this problem, two methods (i.e., PreF and PoF) are applied to generate context-aware collaborator recommendations. Particularly, their main phases (see Fig. 1) can be resumed below, regardless of their order: • Employ D 1 (= U ser), D 2 (= Item), and approaches of 2D recommendations to produce 2D recommendations • Process D 3 ..., D n (= Context) (pre-process in PreF and post-process in PoF) • Produce context-aware recommendations based on the previous results Based on these phases, two corresponding algorithms are constructed (see Algorithms 1 and 2).

•

  Contextual post-filtering (PoF) first utilizes D 1 , D 2 , and approaches of 2D recommendations to produce 2D recommendations. Then D 3 , ..., D n is employed to filter out irrelevant 2D recommendations or adjust their orders, resulting in context-aware recommendations [6]. , D 2 , D 3 , ..., D n inside each phase of the recommendation generation process, which gives rise to truly multidimensional recommendations.

	• Contextual	modeling	(CM) directly processes
	D 1

Such recommendations are mentioned as

2D recommendations in the rest.[START_REF] Mattessich | Collaboration: what makes it work. A review of research literature on factors influencing successful collaboration[END_REF] Here, the context is any information that can be used to characterize the situation of users, items, or interactions between users and items[START_REF] Dey | Understanding and using context[END_REF].Ontology-based Semantic Similarity in GeneratingContext-aware Collaborator Recommendations

A term may be a subject, a predicate, an object or a collection of semantic 3-uples.

Here, x and y are two concepts (instances) in ontologies; O x and O y refer to their sets of ontological features; |O x ∩O y | the number of common features in the sets O x and O y ; |O x | denotes the number of features in the set O x . The range of J(O x , O y ) is [0, 1].

The range of D(O x , O y ) is [0, 1].

Here, O x -O y denotes the relative complement of O y in O x . α, β ≥ 0 are parameters of the Tversky index.

Here, p(x) is the probability of x's appearance in the ontology.

Its range is [0, 1].

For example, if individuals' satisfactions to a collaboration belong to the interval [0, 5], then L Sa = 5.

Algorithm 1: PreF algorithm.

Input: The rating matrix: R, the user: u, the collaboration: c, the set of members in the collaboration c: O c Col , the number of recommendations: K, the number of known collaborations: |X|, the number of users: m. Initialize: Two lists with zeros: SC (of length |X|) and V U (of length m).

by deleting all ratings of irrelevant collaborators v (V U (v ) = 0); 16 for k ∈ {1, 2, .., m} do 17 if R uk is unknown then 18 apply approaches of 2D recommendations to predict users' ratings r * (u, k);

20 Rank R u * in decreasing order and get K highest ratings; Output: User u's ratings R u * , K collaborators with K highest ratings.

Specifically, Algorithm 1 first calculates ontology-based semantic similarities between the collaboration c and other collaborations d (d X, d = c) (line 1-6). Then, it filters out irrelevant collaborators v that did not participate in similar collaborations with c (line 7-15). Next, approaches of 2D recommendations are applied to predict users' ratings for relevant collaborators (line [START_REF] Adomavicius | Incorporating contextual information in recommender systems using a multidimensional approach[END_REF][START_REF] Ricci | Introduction to recommender systems handbook[END_REF][START_REF] Dey | Understanding and using context[END_REF][START_REF] Peckham | Semantic data models[END_REF]. Finally, the top K collaborators with higher ratings will be recommended to the user u (line 20). Briefly, Algorithm 1 first processes the collaboration context by means of the ontology-based semantic similarity, then applies approaches of 2D recommendations, and finally generates context-aware collaborator recommendations for users.

Algorithm 2: PoF algorithm.

Input: The rating matrix: R, the user: u, the collaboration: c, the set of members in the collaboration c: O c Col , the number of recommendations: K, the number of known collaborations: |X|, the number of users: m. Initialize: Two lists with zeros: SC (of length |X|) and V U (of length m).