Jorge Martinez-Gil
email: jorge.martinez-gil@scch.at

Alejandra Lorena Paoletti
email: lorena.paoletti@scch.at

Klaus-Dieter Schewe
email: kd.schewe@scch.at

A Smart Approach for Matching, Learning and Querying Information from the Human Resources Domain

Keywords: e-Recruitment, Knowledge Engineering, Knowledge-based Technology

We face the complex problem of timely, accurate and mutually satisfactory mediation between job offers and suitable applicant profiles by means of semantic processing techniques. In fact, this problem has become a major challenge for all public and private recruitment agencies around the world as well as for employers and job seekers. It is widely agreed that smart algorithms for automatically matching, learning, and querying job offers and candidate profiles will provide a key technology of high importance and impact and will help to counter the lack of skilled labor and/or appropriate job positions for unemployed people. Additionally, such a framework can support global matching aiming at finding an optimal allocation of job seekers to available jobs, which is relevant for independent employment agencies, e.g. in order to reduce unemployment.

Introduction

Some of the major problems concerning the labor market are the complicated situation of the job market in many countries around the world and the increased geographical flexibility of employees. This situation makes companies to often receive a huge number of applications for every open position. Therefore, the costs of manually selecting potential candidates is usually high. For this reason, most companies would like to decrease the costs when publishing job postings and selecting appropriate applicants from such a plethora of potential candidates [START_REF] Bizer | The Impact of Semantic Web Technologies on Job Recruitment Processes[END_REF]. It is also important to remark that unsuccessful job applicants often complain on the lack of transparency in the recruitment processes, and they often wish to receive detailed arguments, or at least, some information about the strengths and flaws of their profiles [START_REF] Thielsch | E-recruiting and fairness: the applicant's point of view[END_REF]. However, they do not receive any kind of feedback very often since this has to be done manually by the other part, and it is quite expensive, in terms of time and resource consumption, for the companies to do that [START_REF] Martinez-Gil | An Overview of Knowledge Management Techniques for e-Recruitment[END_REF].

This complicated situation leads us to think the accurate matching of curriculum vitae (CV) and job offers is very important for employers and job seekers. Therefore, the development of computational methods to optimize the recruitment processes should be of high importance in our current society [START_REF] Malinowski | Matching People and Jobs: A Bilateral Recommendation Approach[END_REF]. Furthermore, such an approach could be beneficial for public and private employment agencies which could perform an analysis to determine the most needed qualification and training courses that would improve the skills of job seekers with respect to the market demands. As a result, a higher occupation rate could be achieved [START_REF] Paoletti | Extending Knowledge-Based Profile Matching in the Human Resources Domain[END_REF].

Currently, existing software solutions in this field are based on syntactic matching, i.e. for a requested profile, existing solutions check how many of the requested terms are overlapped in the candidate profile [START_REF] Mochol | Improving the Accuracy of Job Search with Semantic Techniques[END_REF]. This fact ignores similarity between skills, e.g. programming skills in C++ or Java would be rated similar by a human expert [START_REF] Sanchez | An ontology-based intelligent system for recruitment[END_REF]. Improving this primitive form of matching requires at least taking hierarchical dependencies between education or skill terms into account. To do that, various taxonomies have already been developed such as DISCO competences1 , ISCO2 and ISCED3 . These taxonomies play a central role in our research, since we can exploit them for achieving a more realistic mediation between open employment offers and suitable candidates. Therefore, our major contribution can be summarized as follows:

-We propose here a novel approach for the automatic matching, learning and efficient querying of information from the Human Resources (HR) domain. This approach is based on new methods that appropriately handle traditional limitations, including the uncertainty of human language, the incapability to exploit background knowledge, and the lack of a truly semantic mediation. Additionally, this approach could be of great interest for education and training institutions which could perform analysis to determine the most needed skill sets that would improve the skills of job seekers with respect to the available positions.

The rest of this paper is organized as follows: Section 2 describes the stateof-the-art concerning realistic matching, learning and querying information concerning HR. Section 3 describes the matching problem we are facing and why it is relevant in this context. Section 4 explains how the HR field could be benefit from a framework for learning to rank candidates. Section 5 discusses our approach's capability for querying, and finally, we draw conclusions and put forward future lines of research.

State-of-the-art

The problem of automatically matching job offers and applicant profiles has been studied in the scientific literature [START_REF] Bradley | Personalized information ordering: a case study in online recruitment[END_REF], but the complex nature of the problem we have to face, which involves the use of free text by employers (when writing their job offers) and by employees (when writing their application), makes developed solutions in this context unable to reach a high degree of success [START_REF] Martinez-Gil | An Overview of Knowledge Management Techniques for e-Recruitment[END_REF]. Some works have offered partial solutions based on the use of controlled vocabularies (i.e. ontologies) in order to fairly alleviate some problems concerning semantic heterogeneity [START_REF] Colucci | A Formal Approach to Ontology-Based Semantic Match of Skills Descriptions[END_REF] but there are still some key challenges that should be addressed [START_REF] Racz | Semantic Matching Strategies for Job Recruitment: A Comparison of New and Known Approaches[END_REF].

One of these most important challenges is that the process of matching CVs and job offers is usually done without use of any knowledge base (KB). Instead, overlapping information is computed. In fact, according to the researched literature, a wide range of solutions for job and profiles matching have been addressed by a variety of techniques, ranging from simple bipartite graph matching [START_REF] Farber | An Automated Recommendation Approach to Selection in Personnel Recruitment[END_REF], to vector based techniques taken from classical information retrieval [START_REF] Faliagka | An Integrated E-Recruitment System for Automated Personality Mining and Applicant Ranking[END_REF], to record matching in databases [START_REF] Tinelli | An Innovative Semantic-based Skill Management System Exploiting Standard SQL[END_REF].

Algorithms for bipartite graph matching try to find optimal solutions when trying to maximize the number of matching relation. However, these approaches rely on assigning costs to every match between curriculum and profiles. When the costs are assigned manually, knowledge about them is completely subjective, and therefore it becomes very difficult to revise [START_REF] Cali | A Logic-Based Approach for Matching User Profiles[END_REF]. Moreover, an approach maximizing the number of matches may provide a bad service to users: for example, person P1 could have the best match for job profile J1, but she might be suggested to take job J2 just because J1 is the only available job for person P2 [START_REF] Kuokka | Integrating Information via Matchmaking[END_REF]. This means that from a strictly user-centric viewpoint, maximizing the number of matches is not the feature that could face our problem.

More sophisticated approaches are based on database techniques for record matching [START_REF] Kessler | A hybrid approach to managing job offers and candidates[END_REF] or information retrieval [START_REF] Meo | An XML-Based Multiagent System for Supporting Online Recruitment Services[END_REF]: feature vectors, analytical geometric similarity, weighted criteria, keyword-based search, assessment based on recall and precision [START_REF] Martinez-Gil | Evaluation of two heuristic approaches to solve the ontology meta-matching problem[END_REF]. In case of non-suitable highly ranked profiles human expertise can be used to correct inaccuracies. The problem with these techniques is that they are not suited for dealing with incomplete information usually present in scenarios of this kind. In fact, information about profiles is not always complete, not only because some information is unavailable, but also because some details are considered irrelevant by either the employer or the applicant. Trying to force to use an interface for entering profiles with long and tedious forms to be filled in, is the most often adopted solutions to this problem [START_REF] Straccia | A System for Retrieving Top-k Candidates to Job Positions[END_REF].

Among the problems concerning learning, the task of learning to rank has probably received the most attention in the machine learning literature in recent years. In fact, a number of different ranking problems have been introduced so far. The ranking module is one of the most important modules in a Human Resources Management (HRM) system. For a given job offer there may be hundreds or thousands of relative candidates but only a few of them are to be shown to the expert at a time. Therefore, it is very important to fetch the most relevant candidates and display them to the expert. This means that the way that top candidates are presented decide the success of the HRM system, and therefore, each one of the entries is important.

The major challenge here is to use the expert behavior as a feedback. However, some researchers are skeptical about using this kind behavioral data as a feedback because there are various biases involved in taking behavior into consideration. They show that there exists some presentation bias, which is the bias involved when experts instinctively prefers some candidates in relation to others. It means some candidates are more likely to get better attention from experts and other candidates are not given the proper attention even though they are more relevant. However, it is possible to find useful strategies to solve this bias [START_REF] Joachims | The Value of User Feedback[END_REF].

In practice, when proposing solutions concerning ranking, we think it is a good idea to consider the algorithm Okapi BM25 [START_REF] Robertson | Experimentation as a way of life: Okapi at TREC[END_REF] as the baseline to compare new approaches in this field. The reason to choose an algorithm of this kind is that it is widely used by software systems to rank matching candidates according to their relevance to a given search offer. Okapi BM25 is considered the state-ofthe-art among the methods using a syntactic approach [START_REF] Lv | A Log-Logistic Model-Based Interpretation of TF Normalization of BM25[END_REF]. Therefore, any new method in the field of automatic matching should prove its effectiveness when compared to it.

With respect to querying knowledge bases, in particular in the HR domain, the commonly investigated approach is to find the best k (with k = 1 in most cases) matches for a given profile (applicant profile or job offer) [START_REF] Chakrabarti | Evaluating Refined Queries in Top-k Retrieval Systems[END_REF]. Though this constitutes what is commonly known as top-k-queries, a systematic investigation of such kind of queries is still missing. Top-k-queries have been thoroughly investigated in the field of databases, usually in the context of the relational data model [START_REF] Ilyas | Supporting top-k join queries in relational databases[END_REF], but the study of such queries in the context of knowledge bases has not yet been done. The expectation is of course, that many of the results in the relational data model can be easily adopted to this case. In particular, the focus on a single relation, i.e. the matching, as the driver for the querying, is expected to ease the extension.

In addition to top-k-queries the interest in partial orders in extended matching relations leading to skyline queries as well as global matching optimization and gap analysis place further challenges on matching-related querying of knowledge bases that have not yet been investigated. The classification of most relevant types of queries and the adaptation of corresponding state-of-the-art approaches in databases should be the emphasis in the future. The expected results are supposed to support the efficient answering of such queries.

Matching Information from the Human Resources Domain

In this context, semantic matching is a well know problem whereby two entities in a knowledge base are assigned a score based on the likeness of their meaning [START_REF] Martinez-Gil | Reverse ontology matching[END_REF]. Automatically performing semantic matching is considered to be one of the pillars for many computer related fields since a wide variety of techniques rely on a good performance when determining the meaning of data they work with [START_REF] Martinez-Gil | Automated knowledge base management: A survey[END_REF].

More formally, we can define semantic matching as a function µ 1 x µ 2 → R that associates the degree of correspondence for the entities µ 1 and µ 2 to a score s ∈ R in the range [0, 1] , where a score of 0 states for not correspondence at all, and 1 for total correspondence of the entities µ 1 and µ 2 .

Traditionally, the way to compute the degree of correspondence between entities has been addressed from two different perspectives: using semantic similarity measures and semantic relatedness measures. Fortunately, recent works have clearly defined the scope of each of them. Firstly, semantic similarity is used when determining the taxonomic proximity between entities. For example, automobile and car are similar because the relation between both terms can be defined by means of a taxonomic relation. Secondly, the more general concept of semantic relatedness considers taxonomic and relational proximity. For example, nurse and hospital are not completely similar, but there is still possible to define a naive relation between them because both belong to the world of healthcare [START_REF] Martinez-Gil | Automated knowledge base management: A survey[END_REF].

In most of cases, the problem to face is much more complex since it does not only involve the matching of two individual entities, but two complete documents (applicant profile or job offer). This can be achieved by computing a set of semantic correspondences between individual entities belonging to each of the two documents. A set of semantic correspondences between entities is often called an alignment. It is possible to define formally an alignment A as a set of tuples in the form {(id, µ 1 , µ 2 , r, s)}, where id is an unique identifier for the correspondence, µ 1 and µ 2 are the entities to be compared, r is the kind of relation between them, and s the score in the range [0, 1] stating the degree of correspondence for the relation r.

Therefore, when matching two documents, the challenge that scientists try to address consists of finding an appropriate semantic matching function leading to a high quality alignment between these two knowledge bases. Quality here is measured by means of a function A × A ideal → R × R that associates an alignment A and an ideal alignment A ideal to two real numbers ∈ [0, 1] stating the precision and recall of A in relation to A ideal .

Precision represents the notion of accuracy, that it is to say, states the fraction of retrieved correspondences that are relevant for the matching task (0 stands for no relevant correspondences, and 1 for all correspondences are relevant). Meanwhile, recall represents the notion of completeness, thus, the fraction of relevant correspondences that were retrieved (0 stands for not retrieved correspondences, and 1 for all relevant correspondences were retrieved).

Applying this kind of techniques fits well in the HR scenario. The reason is that these techniques can be used for going beyond the literal lexical match of words. In this way, when analyzing the curriculum of job candidates, this kind of techniques can operate at the conceptual level when comparing specific terms (e.g., Finance) also yields matches on related terms (e.g., Economics, Economic Affairs, Financial Affairs, etc.). As another example, in the healthcare field, an expert on the treatment of cancer could also be considered as an expert on oncology, lymphoma or tumor treatment, etc [START_REF] Chaves-Gonzalez | Evolutionary algorithm based on different semantic similarity functions for synonym recognition in the biomedical domain[END_REF]. The potential of this kind of techniques is that it can support Human Resource Management when leading to a more quickly and easily cut through massive volumes of potential candidate information, but without giving up the way human experts take decisions in the real world.

Learning Information from the Human Resources Domain

The problem of learning can be defined as given a pair of objects (jo, ap i ) together with a measure of their suitability y i ∈ R. The goal is to learn a function f (jo, ap i ) ≈ y i that approximates for every new labeled triplet example (jo, ap i , y i ), where jo is a job offer, ap i is a list of applicant profiles, and y i is the associated list of scores of each ap i for the job offer jo. After many discussions with professionals from the Human Resources sector, we agreed this challenge has not an unique solution. The reason is that every HR professional evaluating different cases could propose different results. This makes us thinking that we should work towards an adaptive approach by means of automatic matching learning. This approach should be able to calculate the transformation cost of a given profile into a requested job offer, so that profiles with higher transformation cost should rank worse than those with lower cost. In this way, our approach should be able to replicate the results from the human experts. This means that for each person aiming to use a solution of this kind, we should train a model for capturing its know-how or preferences by means of an initial training stage. Thinking on a model of this kind is far from being trivial. However, we assume that a generic solution for this problem should be characterized by the following core attributes: a) a base distance between sets, b) some background knowledge to compute the replacement cost, c) the desired cost of insertion and deletion of new elements, d) the way to weight elements, either a multiplicative or an additive preference Please note that if we work with different relevant subsets (education, skills, languages, etc.) the transformations costs could be different for each subset, so the final cost should be an aggregation of the partial costs for each segmented group. Once we get a solution, the way to determine if this solution is satisfactory could be defined as the correlation between this achieved solution and an ideal one.

Concerning a), we can formally define our distance between two sets as the minimum number of single-elements edits (i.e. insertions, deletions or substi-tutions) required to change one set into the other. It is very appropriate for computing the transformation costs from a CV into a job offer.

Concerning b), setting up adequate knowledge bases that capture recruitment terminology in a precise and easily extendable way is a crucial success factor. So far, no such knowledge bases exist. However, our existing matching technology is based on valuable recruitment taxonomies. These taxonomies are structured thesaurus and vocabularies for the description of skills in different scenarios such as the education, job market and training courses respectively. These taxonomies provide us a complete skill and competence classification which is based on existing European and international standards and classifications, and therefore, represent a terminological basis for the standard description of skills, competences, occupations as well as applicant profiles, job vacancies, and job requirements, etc. or for describing professional degrees, study programs, courses, and so on. To illustrate why taxonomies are important for us, let us suppose that a job offer requests a person skilled in Java, and we have a candidate who is skilled in JavaScript. We can compute the shortest path between Java and JavaScript in the recruitment taxonomy. The transformation cost can be based on the length of this path. In this way, short paths leads to low replacement costs, and on the contrary; longer paths may lead to higher replacement costs. If there is no path between them, or even this path is not appropriate enough (i.e. too long) then we can consider insertion and deletion costs.

Concerning c), Suitability of an applicant profile ap i to a job offer jo needs also to consider the minimum cost of element insertions and deletions which transforms the applicant profile ap i into the job offer jo. These costs are going to be used when an applicant profile have a different number of elements than those requested in the job offer or computing the replacement cost between elements is not possible. The computation of these costs is of vital importance because it helps us to characterize the behavior of the people who was involved in the training stage. Insertion cost is an estimation of how much it could cost to a potential candidate to acquire an element requested by the job offer.

Deletion cost is an estimation about the impact of having a not requested element. For example, an expert could think that candidates holding not requested elements could be unhappy, unmotivated, could request a higher salary or be willing to leave the company in a short period of time. The penalty to be applied can be high, if the person in the training phase tends to penalize overqualification, null if the person does not care about additional (although not requested) elements, or even negative, if the person training the model thinks that additional elements are far from hurting. It is also important to note that we cannot have an unique value for insertions and deletions costs. For instance, it is much more expensive (in terms of effort, time and money) acquiring a new university degree that some certain level of mastery in a programming language or technology.

Concerning d) the weighting schema is the way a person could increase or decrease the importance of the elements within a given set. Considering a weighting schema is important because it allows job recruiters giving more importance to some facts like years of experience, level of mastery or simply stating priorities for filling a position.

Querying Information from the Human Resources Domain

One of the main requirements from the HR application domain leads to queries on a knowledge base of job offers and candidate CVs. Ignoring the inherent inferential capability given by knowledge bases. Each knowledge base is also a database in the sense that there is a schema, i.e. the concepts and roles in the TBox, and a set of instances, i.e. the ABox. Therefore, adopting database technology as key method to address the querying problems is a natural idea [START_REF] Paoletti | Extending Knowledge-Based Profile Matching in the Human Resources Domain[END_REF].

In database technology effective and efficient query processing is a core area with a tradition since decades. Recently, two classes of queries, top-k-queries and skyline queries have attracted the interest of researchers [START_REF] Soliman | Supporting ranking queries on uncertain and incomplete data[END_REF]. For top-kqueries assume that a query q produces an answer set A that is totally ordered. Then a query top-k(q) will select the k largest elements of A as the answer. While performing a sorting operation and a cut-off of the largest k elements are straightforward in theory, the key problem with top-k-queries is efficiency on very large databases, for which supporting data structures and rewriting techniques that enable the computation of the k largest answers without computing first all answers. Similarly, skyline queries ask for all maximal elements in an answer set A to a query q, where A is assumed to be partially ordered.

We think that top-k-and skyline queries are essential for the core of matching related queries, where the (partial) order is defined by the matching measures. In case of simultaneous use of several matching measures a partial order may result. Therefore, the key research question is to adopt the solutions from database technology to the area of knowledge bases, which boils down to investigating efficient storage of the ABox including matching measures. For the data structures supporting the subsumption hierarchy it is envisioned that rings and spiders [START_REF] Mylopoulos | Knowledge Bases and Databases: Current Trends and Future Directions[END_REF] known from network databases and revived in object-oriented databases can be adopted. These structures are known for excellent performance in support of queries that exploit hierarchical data structuring. Furthermore, indices based on partial fractions may also be exploited for this purpose [START_REF] Theobald | Top-k Query Evaluation with Probabilistic Guarantees[END_REF].

It is further anticipated that skyline queries will also play an important role for gap analysis, which should result in minimally enlarged filters that guarantee improved matching results. That is, we have to exploit a partial order on filters for such queries. The enlargement itself requires for data structures supporting neighborhoods, which will be a new notion that has to be defined and for which suitable storage representations have to be found. With such extensions it should be possible to exploit state-of-the-art techniques for skyline queries to support the application needs. Furthermore, specific query optimization techniques will be needed.

The adaptation and extension of query optimization is also the method that is needed to support global matching with respect to some optimization criteria. As the optimization criteria will lead again to a partial order, this gives another class of skyline queries, so the remaining problem is efficiency, for which query optimization is due.

Discussion

We think our approach lead to a number of qualitative advantages over the stateof-the-art in this field. These advantages are in the direction of those mentioned in [START_REF] Martinez-Gil | An Overview of Knowledge Management Techniques for e-Recruitment[END_REF]. In fact, we can summarized them in the following four major points: 1. Our approach for realistic matching learning can help players from the HR industry to go beyond syntactical matching of job offers and applicant profiles. This represents a great advantage over the current state-of-the-art since our approach tries to give more opportunities to the good job candidates, but also allows job recruiters to identify potential talent which otherwise may remain blurred among such a plethora of applicants profiles. 2. Our approach can help to eliminate the need for job recruiters to have deep and specialized knowledge within an industry. This is mainly due to this approach is able to model knowledge from a lot of industrial domains. Then this knowledge can be used as a support when performing matching process so that the results can be very similar to those produced by an expert from that field. 3. Our approach can provide feedback to the applicants that did not get the job. The matching process is traceable and this means that some interesting reports can be automatically delivered to the applicants. These reports can help these applicants to determine the reasons they were not selected for the job position as well as to assess their strengths and weaknesses when applying for similar jobs in the future. 4. Our approach allows to leveling the odds for those job applicants with less ability when preparing their resumes. The reason is that an algorithm will perform the matching process automatically. The result from this process is independent of the way the curriculum is presented. Therefore, this technique helps to promote equal opportunities.

Conclusions

We have presented a novel approach for the timely, accurate and mutually satisfactory mediation between open employment offers and suitable candidates. The rationale behind this research approach is to facilitate public and private recruitment agencies as well as employers and job seekers around the world to reduce the costs and time to find relevant matches between job offers and applicant profiles.

The major conclusion we can extract is that an approach of such kind may be able overcome the traditional limitations in this field. 1) Concerning the uncertainty when dealing with natural language: our solution forces to describe either job offers and applicant profiles using a common vocabulary. This fact avoid the problem of dealing with different representations of a same concept. 2) Concerning the incapacity of current approaches to exploit background knowledge: our approach is able to get benefit from external knowledge bases that support our work within the process of making estimations about the cost of acquiring a new skill or competence. 3) Concerning achieving a truly realistic mediation: our approach is able to go beyond syntactic matching of job offers and applicant profiles. Additionally, some practical impact can be envisioned, e.g. capability to reduce unemployment.

As a future work, we plan to develop a benchmark data set in order to assess the quality of the new matching proposals based on this and other different paradigms. The importance of this benchmark data set is high since researchers need some data to test their solutions. One solution could consists of automatically generated random data sets. The problem is that randomly generated data sets are not useful since they do not have realistic distributions, and it is not always easy to understand whether the achieved results are meaningful and correct. Real or quasi-real data is much better in this particular application scenario. For these reasons, we are working towards a benchmark data set that reflects the way real HR experts take decisions in real scenarios and allows research community testing and training new approaches under truly realistic conditions.

http://www.disco-tools.eu

http://www.ilo.org/public/english/bureau/stat/isco/isco08/index.htm

http://www.uis.unesco.org/Education/Pages/international-standard-classificationof-education.aspx

The research reported in this paper was supported by the Austrian Forschungsforderungsgesellschaft (FFG) for the Bridge project Accurate and Efficient Profile Matching in Knowledge Bases (ACEPROM) under contract [FFG: 841284]. The research reported in this paper has been supported by the Austrian Ministry for Transport, Innovation and Technology, the Federal Ministry of Science, Research and Economy, and the Province of Upper Austria in the frame of the COMET center SCCH [FFG: 844597]


Alberto R C Raúl

De Sousa

A Note on Dirichlet's Theorem and GoldBach's Conjecture Proof

Keywords: Dirichlet's Theorem, GoldBach's Strong Conjecture, Proof, Prime Numbers, Complex Wave model, Green-Tao's Theorem. 3 AMS subject classifications 11A41, 11A51, 11P32, 35Q15, 35Q99, 81S99, 81V99

This article presents a alternative and simple proof to the Dirichlet's Theorem and a proof for the Goldbach's Strong Conjecture, using the Complex Wave Model and its properties. The Complex Wave Model allows the definition of an α function based on a sines product. As a consequence of the properties of trigonometric functions, with emphasis to its periodicity and symmetry, some of the questions regarding the prime numbers distribution, k-tuples and prime numbers arithmetic progressions, including the Dirichlet's Theorem and Goldbach's Conjecture, can be solved.

Introduction

As was shown in the article "Prime Numbers: the Particle in the Box and the Complex Wave Model" [START_REF] Alberto | Prime numbers: A particle in a box and the complex wave model[END_REF], it is possible to define a function α(x) which detects prime numbers and coprime numbers relatively to all integers included in the definition of α(x), thus excluding other integers from been prime numbers. This function never generates false negatives, regarding primality testing, and within the √ x limit it also don't generate false positives.

It was also identified patterns in the distribution of primes and coprime, that thins out towards infinity. These patterns are periodic with its smaller period represented by the product of the first prime factor of each integer included in alpha s definition. If only and all prime number are used up to a certain N, then the product will be equal to the primorial of N.

It was also stated that the patterns generated by α function can represent any k-tuples, arithmetic progressions and all kind of polynomial that generates primes. In this article, α function will be used to provide an alternative and simple proof to the Dirichlet's theorem and to provide a definitive prove to the Goldbach's strong conjecture.

Dirichlet's Theorem

In 1837, Dirichlet put forward one of his most famous theorem stating that: "For any two positive coprime integers a and d, there are infinitely many primes of the form a + nd, where n is a non-negative integer." Dirichlet used the characters of finite abelian groups and L-series to prove the theorem presented above. The proof that Dirichlet presented is extremely technical and long. An alternative proof has been presented by Haifeng Xu [START_REF] Xu | An alternative proof of the dirichlet prime number theorem[END_REF], through sieving analysis and induction. This inductive analysis allows the identification of periodicity and symmetry in prime number candidates. These properties were formally demonstrated by Raúl de Sousa through a alternative method using a sines product named Complex Wave Model. [START_REF] Alberto | Prime numbers: A particle in a box and the complex wave model[END_REF]. The α function periodicity is of great importance in providing an alternative and simpler proof for the Dirichlet's Theorem, as it will be demonstrated.

Proof. Let us consider an α function defined as follows:

For all x, k and N ∈ integers,

α(x) : l m=k sin π m x (1)
It is evident that α(x) is a periodic function due to the definition of α(x) as an sines product, with its period been:

τ = p x 1 p y 2 ...p z n (2)
x, y,..., z represents the number of times that its p i is the lowest prime factor of every integer from k to l.

A note for τ definition and its coincidence with the Fundamental Theorem of Arithmetic, that states every positive integer n > 1 can be represented in an unique product of prime powers. This will be useful further on in this article, regarding the Goldbach's Strong Conjecture.

If we use all PN from 2 up to N in α(x), then τ is the primorial of N:

τ = N (3)
If we use in α(x), any number N, then τ is the radical of N, being the radical of any integer the product of the distinct prime numbers dividing N:

τ = Rad(N) (4)
If k = 2 and all integers up to l are included in the α(x), all α's solutions different from zero will signal all primes for l < x ≤ l 2 and candidates to primes for x > l 2 . These solutions are coprimes to all integers from k to l, by definition, and include all prime numbers besides the ones in k to l, as well. Another way to stated the same is stating that all candidates to prime are coprime to τ since τ is an integer product from k up to l.

Been α(x) a periodic function, we have that α(x) = α(τ + x), meaning that all solutions of α(x) 0 from x =0 to ∞ are coprime to the set k,...,N and have the form:

x + nτ and x, τ are coprimes for every n ∈ Integers.

(5)

Since it has stated in the second Complex Wave Theorem that all primes numbers are included in the α(x) 0 solutions. It implies that all prime numbers have the Dirichlet's Theorem form 5 and that there are infinite n for which that the linear polynomial x + nτ produces prime numbers, thus demonstrating the Dirichlet's Theorem.

Regarding Green-Tao's Theorem, it is evident that we can choose any x and any τ so that, we can obtain arbitrarily, but finite, long arithmetic progressions of prime numbers interrupted by non-primes, that are coprimes to x and every factor in τ.

From the periodicity property of α(x), a very significant conclusion is dawned. All prime numbers have to be in the form P x + kτ = P y where τ is coprime to P x and P y , although not all numbers in the P x + kτ are prime numbers.

GoldBach's Strong Conjecture

The Goldbach's Strong, or Binary, conjecture stated by Euler asserts that all positive even integers greater than 4, represented by N, can be expressed as the sum of two prime numbers P y , P x : P y + P x = N. Although the GoldBach's Weak, or Ternary, conjecture has been prove by H. A. Helfgott, the Strong conjecture remains to be proven.

Another way to put the Goldbach's Strong conjecture is to state that, for all even N there exists at least one set of two prime numbers, P y and P x , at the same distance from N 2 . In other words, there exist at least one pair of prime numbers symmetric to N 2 . Please note that P y = P x is also a solution, which implies that P y = P x = N 2 . The symmetry pattern in the prime numbers location identified by the α(x) 0, can demonstrate the existence of the required type of symmetry in the prime numbers distribution, for all even numbers equal or above 4, as follows.

Proof. As showed above, α(x) is periodic. Also, because α(x) is a product of sines, it is implied that α(x) is symmetric to τ 2 . This symmetry property was also been pointed by Haifeng Xu [START_REF] Xu | An alternative proof of the dirichlet prime number theorem[END_REF], by inductive analysis of the Eratostones Sieve. Therefore, the prime numbers candidates, which includes all prime numbers besides the ones included in α(x), therefore in τ, are symmetric to τ 2 . Since that the possible locations for prime numbers through the pattern repetition can not change, there must be at least one prime number among the prime numbers candidates on the second half of τ, symmetrical to a prime number in the first half. If it was not the case, that would mean that there were not anymore locations for further prime numbers, thus implying the false conclusion that the Prime Numbers' set was to be finite.

It is possible to classify α(x) as a even function if the set cardinal #a, ..., N is even and as an odd function if the set cardinal is odd. Since we are only interested in the center of symmetry, we can generalize and state that:

|α(x)| = |α(τ -x)|, (6)
with the center of symmetry been τ 2 . As already stated, one implication of this symmetry is that for every x solution to α 0, exists a τx that is also solution to α 0 including all prime numbers that are not used in the α(x)

With a simple observation of the τ product, it is easy to verify that it has the form stated in the Arithmetic Fundamental Theorem, and in its short period is equal to the radical of an integer 4. A consequence of that observation is that any number can be chosen to be the τ and, therefore, to construct an α(x) function.

So, we can write the unique integer factorization of any even number N and use those factors to define the set {P x , P y , ...} for the {k, ..., l} of an α(x), so that τ is equal to the chosen even number N with α(x) defined as α p x ,p y ,... (x). Every x that is solution for α 0 is coprime to the set {P x , P y , ...} as it is, also, its symmetric taux to the period τ = N. Since all prime numbers have to be solution to α(x) 0 and none is excluded, it implies that for every even N there exists N = P x + P y .

Recalling eq. 4, it can be defined an α Rad(N) (x) so that the solutions for α Rad(N) (x) 0 includes, at least, one set of prime numbers that are symmetric to τ 2 , proving the Golbach's Strong Conjecture.

From the symmetry property of α(x), a very significant conclusion is dawned. All prime numbers have to be in the form τ -P x = P y where τ is coprime to P x and P y , although not all numbers in the τ -P x are prime numbers.


Jiliang Wang

Bernard Yannou

A MARKET SEGMENTATION PROCESS BASED ON USAGE CONTEXT

Keywords: usage model, usage context, market segmentation, cluster analysis

Designing an appropriate product or service requires to know the targeted markets. Traditionally, market segmentation methods are based on socio-demographic data. In many situations, it is not sufficient enough to elicit relevant segments with clear orientations. We propose here to add usage context data so as to define relevant market segments before leading kansei studies in each segment. The case study of cutting a wood board with a jigsaw tool is taken in order to exemplify how usage context variables may influence segments.

INTRODUCTION

The analysis of customer's requirements and preferences is an important stage for product design. Due to limits of company's budget and marketing strategy, managers are always willing to choose profitable segments as target market segments for launching new products or redesigning existing products. Prediction of the profit for a given product in a given market segmentation is essential for the decision model of a company. In turn, it requires to model the demand to model the cost. So the precision of market segmentation, which determines the quality of demand prediction, becomes especially important. Market segmentation consists in defining homogeneous groups of customers and it is one of the building blocks of effective product or product family positioning. Products or services can no longer be designed and sold without considering customer needs and recognizing the heterogeneity of those needs. Various statistical techniques are available in order to identify market segments, among these, cluster analysis and latent class models. For the segmentation variables, traditional market segmentation methods are always based on marketing attributes and demographic attributes of customer, or correlations between them [START_REF] Green | A guide to market segmentation[END_REF]. Nowadays furious market competition requires that companies design specific products for specific customer segments. Only slight differences from the competitors' solutions may lead to great successes if actual customers' requirements are captured. Traditional market segmentation modeling could not distinguish such latent attributes. Moreover, as customers become more conscious of their expectations on the products, markets often continue to be ever more fragmented into more technical niches. Exploiting the rich contextual information which exists in customers' product usage becomes more and more crucial for product design, especially in the situation that the customer is experienced and able to imagine the probable performances of the product regarding to their usage. As a result, traditional marketing segmentation methods should be extended to contain contextual attributes, in order to drive more efficient kansei analysis in each context segment.

In this paper, we begin by a general literature review of usage context models and market segmentation methods in research. Next, we present the basic principles behind our general usage model and show how it may be integrated into a method of market segmentation. Finally, we apply the usage context market segmentation method in a brief case study of cutting a wood board with a jigsaw tool in order to exemplify how usage context variables may influence segments. We conclude by reaffirming the utility of this integrated method and outlining the further research work that will be done in the future.

STAT-OF-THE-ART AND OBJECTIVE OF RESEARCH

Segmentation is a grouping task for which a large variety of methods are available. Segmentation methods can be classified in a-priori, when the type and number of segments are determined in advance by the researcher, and post-hoc, when the type and number of segments are determined on the basis of results of data analysis. Clustering methods are the most popular tools for descriptive segmentation both in research and industrial applications [START_REF] Bassi | Latent class factor model for market segmentation[END_REF]. They are employed extensively in segmentations based on psychographics, benefits seeking or conjoint partworth data [START_REF] Green | Segmenting markets with conjoint analysis[END_REF]. In general, researchers want to find individual segments that are internally as much homogeneous as possible. K-means cluster analysis is the most frequently used to find homogenous segments of customer, since it can accommodate the large sample size with market segmentation studies. A comprehensive review of K-means methods and of more efficient genetic combined K-mean methods can be found in [START_REF] Kuo | Integration of self-organizing feature maps neural network and genetic Kmean algorithm for market segmentation[END_REF].

The needs of customer may be considered as Direct Needs and Latent Needs. Direct Needs are those that customers have no problem to express as something they are concerned about when sollicitated to talk about the product. Latent Needs are typically not directly expressed by customers, then some stimulations must be done for customers to talk about [START_REF] Otto | Product Desing: Techniques in Reverse Engineering and New Product Development[END_REF]. Usage contextual information contains and reflects user's unrevealed requirements during product application. Meanwhile, designer can comprehend the contextual information and help user probing these latent needs. Context is any information that can be used to characterize the situation of a person, place, or object that is considered relevant to the interaction between a user and an application, including the user and applications themselves [START_REF] Anind | Understanding and Using Context[END_REF]. While the formal study of usage context permeated the field of marketing years ago, it has only just begun to be applied directly to the design and engineering of new products. Green et al. have published three successive papers on the subject [START_REF] Green | Product Usage Context: Improving Customer Needs Gathering and Design Target Setting[END_REF][8] [START_REF] Green | Frontier Design: A Product Usage Context Method[END_REF], with the goal of forming a comprehensive product design methodology that includes contextual factors. In these papers, important first steps in the field were taken, including the definition of key terms and concepts in design engineering: "usage context, as it relates specifically to products, is defined as the unique combination of application and environment in which a product is used." Furthermore, usage context is framed as one part of a larger product design context, which also includes market and customer context [START_REF] Green | Frontier Design: A Product Usage Context Method[END_REF]. During the course of the studies, customers were found to have distinct product preferences under different usage contexts. In the domain of hi-tech product design, context-aware systems -knowing the activity context and taking it into account for system behavior -are emerged. Context-aware system for mobile cartography has been shown in [START_REF] Reichenbacher | Adaptive Methods For Mobile Cartograph[END_REF], which uses formalization to describe situations and contexts for finding typical context patterns. Additionally, evidence supported that contexts could be differentiated based upon functional attributes, indicating a link between engineering parameters and perceived usefulness, which occurs under the influence of different usage contexts.

So our objective in this paper is to investigate deeply the product contextual information and integrate it while segmenting market with cluster analysis method. Latent requirement pattern can be found from resulting segments. In each context segment, customers' usage behavior and demographic attributes are quite homogeneous, which could serve as a basis for future kansei analysis or further experiments.

MODEL AND METHODS

Usage Context Model

We have proposed a Usage Context Model so as to get a more thorough marketing model based on sets of permitted usages for a product-service instead of the conventional perceived marketing attributes [START_REF] Yannou | Usage coverage model for choice modeling: principles[END_REF]. In this model, customers are understood as product employers and products as service providers. This method proposes to quantify individuals' performances during product usage, depending on the usage context and on the personal skills of the individuals. It offers the advantage of linking with user experience to introduce the perceived quality of a product's service, as well as to consider particular service delivery conditions.

In our usage context model, a product is defined by its design parameters X, such as physical dimensions of product. Variable set E represents any variables that describe the conditions under which the product is used to provide the service; this is the usage context. Cs are user-related parameters that affect performances. Then one states that individuals' performances Y during product usage depend on the product itself X, on the context E and on the user's skills Cs. Such performance equations could either be obtained by physics-based model or rating-based regression model.

( ) , , s Y f X E C =

A usage needed is defined as a set of expected service contexts Ei associated with a usage percentage Fi.

( ) { }

,

needed i i U E F =
The usage context E consists of the environment of usage and the object of usage. One example of building UCM for the situation of using jigsaw to cut wood boards or sticks is illustrated in the work [START_REF] Yannou | Usage coverage model for choice modeling: principles[END_REF], where performance values are established using a physics-based model.

Process of Usage Context Information Collection

The process of usage context information collection is very crucial for the whole usage context based market segmentation process. Because the kind of contextual information collected and its quantity play an important role in the following clustering process. Figure 1 reveals the principal stages of this process. First of all a brainstorming is carried out among design team members to identify the important usage context variables. Brainstorming is well-known for generating a flood of new ideas, in which a group of open-minded designers from different spheres of life bring up any thoughts that are related to usage context variables of a given product. These variables can describe properly the conditions under which the product is used to provide the service.

The intervals of the context variables are identified by interviews with experts: here design team members discuss the usage context information one single customer at a time. The interviewed customers are chosen to be "experts" on the product usage. They can estimate the importance of each context variable and its possible interval value. The interviews are held in the customer's environment, where the customer uses the product. The design team records the customer responses.

In the questionnaire, the team develops a list of criteria it believes relevant to the customer's concerns and organizes a customer panel for responses. The collected questionnaires are treated and translated to ordinal data for further cluster analysis process. A process example of jigsaw product case study is shown in the following section.

Cluster Analysis for Usage Context Segmentation

In order to ultimately find out profitable segments for product design, only the individual decision is insufficient. For instance, the customers with similar usage contexts for whom a single type of saw may be designed and marketed in case of cutting wood requirement. Interior homogeneous segments should be built first. Cluster analysis can be conducted to find similar segments of a population based on Environmental Context (E), User skill (Cs), Demographic attributes (S), or the complete set [E, Cs, S]. The following cluster types were examined from a hypothetical data set created for that aim:

-Clustering by Object (subset of E).

-Clustering by Environment (subset of E).

-Clustering by Skill and Demographics (Cs, S) -Clustering by All attributes (E, Cs, S).

Usage similarity must take all usage environments and skill level attributes into account. Two methods are used for identifying similar usage segments: Latent Class Analysis, used when the usage attributes are categorical (e.g. type of wood) or ordinal (e.g. skill level on a scale of 1-3) measures. Latent class analysis enables a characterization of categorical latent (unobserved) variables from an analysis of the structure of the relationships among several categorical manifest (observed) variables. Maximum likelihood estimates (MLEs) of the conditional and latent class probabilities is calculated. [START_REF] Allan | Mccuthcheon Latent Class Analysis[END_REF]. Cluster Analysis when the usage variables are continuous (e.g. thickness of cut to be made). These methods are capable of identifying the optimal number of latent classes or clusters, and all the usage contexts which belong to each latent class or cluster.

EXPERIMENTATION

An example of "cutting wood sticks and boards" service is used. A given user may use a given saw tool. The experimental activities intend to reveal the usage context variables.

Saw Service Usage Context Information Identification and Collection

A brainstorming within the research group is carried out to identify the relevant saw usage context variables, so do several expert experiments to identify possible value interval.

{ }

Yes/No Workbench ∈

The customer related attributes S may influence preference of product, such as income, etc. Cs in saw case is user-related parameters that affect performances, but not preference, e.g. user's skill. While some user related parameters can belong to both types, e.g. gender.

A panel of users gives their opinions for their usage context information by answering a questionnaire which requires simply choosing among several categories about their usage of jigsaw. The sample questionnaire is shown in the Appendix A, which supposes that all the users are given a product of jigsaw BOSCH with specification X. An example of questionnaire for single usage situation can be found at: http://www.diaochapai.com/c3da8833-6005-4ba9-9104-add2e357c733; Internet version eases the collection of survey information.

The semantic answers of the responders are translated into ordinal values. A matrix of each user's usage context and demographic pattern is build based on their answer sheet. Appendix B shows an example of simulated answer data of 30 users on their typical (single) usage information and their demographic information.

Cluster Analysis for Usage Context Information

First of all, a two-step clustering method is carried out to find a relative good final number of clusters. The main process of two-step clustering is to group cases into pre-clusters, and then standard hierarchical clustering is applied to the pre-clusters in the second step. This method is used when one or more of the variables are categorical (not interval or dichotomous). We have assumed that data are interval in level or are true dichotomies for hierarchical and k-means clustering, though twostep clustering can handle categorical data. So when at least one variable is categorical, two-step clustering must be used. One experimental hypothesis is that all observations are independent. Randomization of cases is recommended. Because K-means and two-stage cluster analysis usually generate different solutions, depending on the sequence of observations in the dataset.

We have try SPSS for our case with usage context variables. Since our variables are mainly categorical, only the process of two-step clustering is applicable. The process gives final classes based on preset criteria. If we let the process choose the final clusters, based on Akaike's information criterion (AIC), a measure of the goodness of fit of an estimated statistical model. Given a data set, several competing models may be ranked according to their AIC (see Figure 3), with the one having the lowest AIC being the best. We can see from the resulting table of Figure 3 that 6 clusters satisfy the AIC criterion. So another constrained two step cluster analysis is carried out with SPSS to find the 6 optimal clusters. Table 1 shows how the 30 response cases are distributed in the 6 final clusters. The 6 typical usage context and demographical combined clusters are detailed in table 2. As one may notice, the possible combinatory of attributes is huge, but the number of clusters is finally acceptable. Our method can transform a large number of usage and user information into a manageable number of usage patterns. Extreme and abnormal usage context situations with very few users are merged with similar usage segments. Finally, six typical usage and user patterns are derived: with certain attributes extremely similar, while other attributes can be little variant. The identical attributes will dominate as the number of survey increases. Take the example of last usage context segment: -Medium skill female user, cutting medium thickness stick, without workbench; but their hardness, size, location, lighting, income can take a spectral value, which leads to several merges when one considers design products for this niche.

As a result, market segmentation should be based on usage context and demographic attributes. The practical application of such a method is shown in the case, for example, assuring that members of a cluster are similar on several measures and would therefore all be more likely to prefer the same saw design. For example, if we exclude demographics from the clusters, we may design a saw that meets the object and environment context well for a given cluster, but may only appeal to a certain income segment within the cluster.

CONCLUSION AND PERSPECTIVES

In this paper, we integrate usage context information in traditional market segmentation methods. Cluster analysis is performed to different type of segment decision variables. As shown in the results, segmentation method which integrates usage model performs complete market segments, which are internally homogeneous. Different usage context patterns can be found from the results. Within each of these usage context patterns, a kansei analysis process may be carried out according to better investigate perceptual and emotional users' expectations.

APPENDIX A: SAMPLE SURVEY QUESTIONAIRE TO IDENTIFY E, CS, S

------------------------------------------------------------------------------------------------------Assume that you are given a jigsaw BOSCH as shown in the picture. What is your most usual usage context when you cut a piece of wood? Pleas answer the following questions:

Figure 1 :

 1 Figure 1: Process of Usage Context Information Collection

Figure 2 :•••

 2 Figure 2: Saw Service ExperimentsThe service context variables E may be:

Figure 3 :

 3 Figure 3: Auto-Clustering results of AIC

Table 1 :

 1 Two Step Cluster Analysis Results

Table 2 :

 2 The 6 typical usage context and demographical combined clusters ID Hardness Size Thickness Form Location Lighting Workbench Gender Incomes Skill -Skilled user, in apartment, cutting small hard thin stick, with lighting and workbench

	1	1	1	1	2	1	1	1	1	3	3
	7	1	1	1	2	1	1	1	1	1	2
	16	1	1	1	2	2	1	2	2	1	3
	29	1	3	1	2	1	1	1	2	1	3
	-Medium skill female user, cutting large thick board, with lighting and workbench
	6	2	3	3	1	1	1	1	2	1	2
	12	2	3	3	1	2	1	1	2	1	2
	15	2	3	3	1	1	1	1	2	2	2
	21	1	2	3	1	1	1	1	2	2	3
	28	1	1	2	1	2	1	1	2	2	2
	-Beginner male user, cutting thick board, with lighting and workbench
	2	1	3	3	1	1	1	1	1	1	1
	4	1	2	3	1	2	2	1	1	1	3
	10	2	3	3	1	1	1	1	1	3	1
	14	2	3	3	1	1	1	1	1	3	1
	19	1	2	3	1	2	1	1	1	1	1
	23	2	2	3	1	1	1	1	1	2	1
	25	1	3	3	1	1	1	2	2	1	1
	-Male medium income user, cutting thin stick in apartment, without lighting, with workbench
	9	1	2	1	2	1	2	1	1	2	3
	17	3	3	1	2	1	2	1	1	2	1
	24	3	3	1	2	2	1	1	1	2	3
	27	1	2	2	2	1	2	2	1	2	1
	-Medium skill male user, cutting thick board, without lighting and workbench
	5	2	3	3	1	1	2	2	1	2	1
	11	2	2	3	1	1	2	2	1	3	2
	18	1	3	2	1	1	2	2	1	2	2
	22	1	1	3	1	2	2	2	1	2	2
	26	2	1	3	1	2	2	1	1	3	2
	30	1	3	3	1	1	2	2	1	1	2
	-Medium skill female user, cutting medium thickness stick, without workbench
	3	2	2	2	2	1	1	2	2	2	2
	8	3	3	2	2	2	1	2	2	1	1
	13	3	3	2	2	2	2	2	2	2	2
	20	1	2	2	2	1	2	2	2	1	2

1. Please tell us a little bit about yourself: o

  Are you: □ ,. male □ ,. female o What is your skill level in terms of saw usage? □ ,. Beginner □ ,. Intermediate □ ,. Experienced

	o What is your monthly income?
	□ ,. Low (<1000€ )	□ ,. Medium (1000€ ~3000€ )	□ ,. High (>3000€ )
	2.
	o Where do you live in?
	□ ,. Apartment	□ ,. House
	o Is there lighting system when you are doing your saw job?
	□ ,. Yes	□ ,.No
	o Do you have a workbench while you cutting wood?
	□ ,. Yes	□ ,.No

Please tell us about your typical saw usage situation: o What kind of wood hardness do you mostly cut with a jigsaw? □ ,. Soft wood □ ,. Intermediate □ ,. Hard wood o What kind of size do you usually cutting with a jigsaw? □ ,. Small size □ ,. Intermediate □ ,. Large size o What thickness of wood do you mostly cut with a jigsaw? □ ,. Thin □ ,. Intermediate □ ,. Thick o What type form of wood do you mostly cut with a jigsaw? □ ,. Board □ ,. Stick

APPENDIX B: QUESTIONAIRE RESPONSES DATA

ID Hardness Size Thickness Form Location Lighting Workbench Gender Incomes Skill


El Moatez

Billah Nagoudi

Jérémy Ferrero

Didier Schwab
email: didier.schwab@imag.fr

Hadda Cherroun
email: h.cherroun@lagh-univ.dzjeremy.ferrero

Word Embedding-Based Approaches for Measuring Semantic Similarity of Arabic-English Sentences

Keywords: Semantic Sentences Similarity, Cross-Language, Arabic-English, Machine Translation, Word Embedding. MT-Based Models Kent and Salim [18], Muhr et -CL-AES [3], CL-PDAE [2] Comparable Corpora-Based Models CL-KGA [11], CL-ESA [12]

Semantic Textual Similarity (STS) is an important component in many Natural Language Processing (NLP) applications, and plays an important role in diverse areas such as information retrieval, machine translation, information extraction and plagiarism detection. In this paper we propose two word embeddingbased approaches devoted to measuring the semantic similarity between Arabic-English cross-language sentences. The main idea is to exploit Machine Translation (MT) and an improved word embedding representations in order to capture the syntactic and semantic properties of words. MT is used to translate English sentences into Arabic language in order to apply a classical monolingual comparison. Afterwards, two word embedding-based methods are developed to rate the semantic similarity. Additionally, Words Alignment (WA), Inverse Document Frequency (IDF) and Part-of-Speech (POS) weighting are applied on the examined sentences to support the identification of words that are most descriptive in each sentence. The performances of our approaches are evaluated on a crosslanguage dataset containing more than 2400 Arabic-English pairs of sentence. Moreover, the proposed methods are confirmed through the Pearson correlation between our similarity scores and human ratings.

Introduction

Semantic Textual Similarity (STS) is the task of measuring the degree of semantic equivalence between two textual units (texts, paragraphs or sentences) [START_REF] Agirre | Semeval-2016 task 1: Semantic textual similarity, monolingual and cross-lingual evaluation[END_REF]. STS is a core field of Natural Language Processing (NLP) and plays an important role in several application areas, such as Information Retrieval (IR), Word Sense Disambiguation (WSD), Question Answering (QA), and Text Summarization (TS) among others. There are two known types of STS: monolingual and cross-language [START_REF] Alzahrani | Cross-language semantic similarity of arabic-english short phrases and sentences[END_REF]. The first one estimates the degree to which the underlying semantics of two textual units written in the same language, are equivalent to each other, while the STS cross-language aims to quantify the degree to which two textual units are semantically related, independent of the languages they are written in [START_REF] Gupta | Cross-language high similarity search using a conceptual thesaurus[END_REF].

Determining the similarity between sentences has been extensively reviewed in a monolingual domain [START_REF] Li | Sentence similarity based on semantic nets and corpus statistics[END_REF], [START_REF] Är | Ukp: Computing semantic textual similarity by combining multiple content similarity measures[END_REF], [START_REF] Rios | Uow: Multi-task learning gaussian process for semantic textual similarity[END_REF] and [START_REF] Wali | Enhancing the sentence similarity measure by semantic and syntactico-semantic knowledge[END_REF]. While cross-language semantic similarity is relatively more difficult to identify since the relatedness of words are investigated between two different languages [START_REF] Gupta | Cross-language high similarity search using a conceptual thesaurus[END_REF]. Thus, it is necessary to address this task to enhance the performance in several applications, such as Machine Translation (MT), Cross-Language Plagiarism Detection (CLPD) and Cross-Language Information Retrieval (CLIR).

In this paper we focus our investigation on measuring the semantic similarity between Arabic-English cross-language sentences using machine translation and word embedding representations. We also consider words alignment, term frequency weighting and Part-of-Speech tagging to improve the identification of words that are highly descriptive in each sentence.

The rest of this paper is organized as follows, the next section describes work related to STS cross-language detection and word embedding models. In Section 3, we present our proposed cross-language word embedding-based methods. Section 4 describes the experimental results of these systems. Finally, our conclusion and some future research directions are drawn in Section 5.

Related Work

In this section, we review the most relevant approaches for measuring cross-language semantic textual. Then, we study those dedicated to the Arabic-English semantic similarity. Finally, we recall some concepts related to word embedding.

Cross-Language Semantic Textual Similarity Detection

In the literature, many approaches are proposed for cross-language textual similarity detection. We can classify them according to the strategy they used to detect such similarity into five classes: Syntax-Based, Dictionary-Based, Parallel and Comparable Corpora-Based and MT-Based Models [START_REF] Ferrero | A multilingual, multi-style and multi-granularity dataset for cross-language textual similarity detection[END_REF]. Figure 1 shows the taxonomy of different approaches for cross-language similarity detection. In the following, we will review the most commonly used methods.

Concerning the syntax-based models, the key idea lies in comparing multilingual texts without translation. For instance, Pouliquen et al. [START_REF] Happe | Automatic concept extraction from spoken medical reports[END_REF] have proposed a "Length Model" to estimate cross-language text similarity. It is mainly based on comparing the texts size. They observed the fact that the length of texts in different languages are closely linked by a factor, and there is a different factor for each language pair. McNamee and Mayfield [START_REF] Mcnamee | Character n-gram tokenization for european language text retrieval[END_REF] have introduced Cross-Language Character N-Gram (CL-CNG) model to compare two textual units by using their n-gram vectors representation. This technique achieves a good performance with languages that are close to each other, because of common root words.

In dictionary-based models, the semantic similarity is measured by constructing a vector space model of the textual units. For that, a vector of concepts is built for each textual unit using dictionaries or thesaurus. The similarity between the vectors of concepts can be measured using the Cosine similarity, Euclidean distance, or any Fig. 1: Taxonomy of different approaches for cross-language similarity detection [START_REF] Ferrero | A multilingual, multi-style and multi-granularity dataset for cross-language textual similarity detection[END_REF]. other similarity measure. In [START_REF] Gupta | Cross-language high similarity search using a conceptual thesaurus[END_REF] a Cross-Language Conceptual Thesaurus-Based Similarity model (CL-CTS) is proposed to measure the similarity between textual units written in different languages (Spanish, English and German). CL-CTS is based on the thesaurus concepts vectors presented in Eurovoc1 where a Cosine similarity is computed between these vectors. In the same context, Pataki [START_REF] Pataki | A new approach for searching translated plagiarism[END_REF] have proposed a Cross-Language Dictionary-Based Language-Independent (CL-DBLI) model. CL-DBLI considers a translation synonym dictionary to extract the abstract concepts from words in textual units.

For comparable corpora-based models, Gabrilovich and Markovitch [START_REF] Gabrilovich | Computing Semantic Relatedness using Wikipedia-based Explicit Semantic Analysis[END_REF] have presented a Cross-Language Explicit Semantic Analysis (CL-ESA) model. CL-ESA is based on the Explicit Semantic Analysis (ESA), which represent the meaning of text by a vector of concepts derived from Wikipedia. In a cross-lingual context, Potthast et al. [START_REF] Potthast | A Wikipedia-Based Multilingual Retrieval Model[END_REF] use Wikipedia as comparable corpus to estimate the similarity of two documents by calculating the similarity of their two ESA representations. Another model called Cross-Language Knowledge Graph Analysis (CL-KGA), is introduced for the first time by Franco-Salvador et al. [START_REF] Franco-Salvador | Cross-language plagiarism detection using a multilingual semantic network[END_REF]. CL-KGA uses knowledge graphs built from multilingual semantic network (the authors use BabelNet [START_REF] Navigli | BabelNet: The automatic construction, evaluation and application of a wide-coverage multilingual semantic network[END_REF]) to represent texts, and then compare them in a common lingual semantic graph space.

Regarding parallel corpora-based models, several approaches are proposed. For instance, Barrón-Cedeño et al. [START_REF] Barr Ón-Cedeno | On cross-lingual plagiarism analysis using a statistical model[END_REF] have introduced a Cross-Language Alignment Similarity Analysis (CL-ASA) approach. CL-ASA estimates the similarity between two textual units using bilingual statistical dictionary extracted from parallel corpus. The same idea was used independently by Pinto et al. [START_REF] Pinto | A statistical approach to crosslingual natural language tasks[END_REF]. A Cross-Language Latent Semantic Indexing model (CL-LSI) is developed by Potthast et al. [START_REF] Potthast | Cross-language plagiarism detection[END_REF]. CL-LSI uses a parallel corpora with the common Latent Semantic strategy applied in IR systems for term-textual unit association. Another model named Cross-Language Kernel Canonical Correlation Analysis (CL-KCCA) model due to Vinokourov et al. [START_REF] Vinokourov | Inferring a Semantic Representation of Text via Cross-Language Correlation Analysis[END_REF], it analyzes the correspondences between two LSI spaces to measure the correlation of the respective projection values.

The main idea of the machine translation-based models consists in using MT tools to translate textual units into the same language (pivot language) in order to apply a monolingual comparison between them [START_REF] Ño | Methods for cross-language plagiarism detection[END_REF]. For this purpose, Kent and Salim [START_REF] Kent | Web based cross language plagiarism detection[END_REF] have used Google Translate API to translate texts, while Muhr et al. [START_REF] Muhr | External and intrinsic plagiarism detection using a cross-lingual retrieval and segmentation system[END_REF] replace each word of the original text by its most likely translations in the target language.

Arabic-English Cross-language Semantic Similarity

In context of the Arabic-English cross-language semantic similarity, Hattab [START_REF] Hattab | Cross-language plagiarism detection method: Arabic vs. english[END_REF] has used Latent Semantic Indexing (LSI) to build cross-language Arabic-English semantic space (CL-AE-LSI), from which it checks the contextual similarity of two given texts, one in Arabic and the other in English.

Recently, Alzahrani [START_REF] Alzahrani | Cross-language semantic similarity of arabic-english short phrases and sentences[END_REF] presented two models of Semantic Similarity for Arabic-English Cross-Language Sentences (SS-CL-AES). The first one used a dictionary-based translation, where an Arabic sentence is translated into English terms, then the semantic similarity is computed by using the maximum-translation similarity technique. In the second model, MT is applied on the Arabic sentence. After that, the algorithms proposed by Lee [START_REF] Lee | A novel sentence similarity measure for semantic-based expert systems[END_REF], and Liu et al. [START_REF] Liu | Gplag: detection of software plagiarism by program dependence graph analysis[END_REF] are used to calculate the semantic similarity.

Alaa et al. [START_REF] Alaa | Cross-language plagiarism of arabicenglish documents using linear logistic regression[END_REF] are interested in Cross-Language Plagiarism Detection of Arabic-English documents (CL-PDAE). In fact, after a candidate document retrieval step by key phrase extraction, they translate a source text by getting for a word all the available translations of all its available synonyms from WordNet [START_REF] Miller | Wordnet: a lexical database for english[END_REF], and then they use a combination of monolingual measures (Longest Common Subsequence (LCS), Cosine similarity and N-Gram) to detect similar phrases.

Word Embedding-Based Models

Recently, Word Embedding (WE) technique has received a lot of attention in the NLP community and has become a core building to many NLP applications. WE represents words as vectors in a continuous high-dimensional space. These representations allow capturing semantic and syntactic properties of the language [START_REF] Mikolov | Efficient estimation of word representations in vector space[END_REF]. In the literature, several techniques are proposed to build word embedding models.

For instance, Collobert and Weston [START_REF] Collobert | A unified architecture for natural language processing: Deep neural networks with multitask learning[END_REF] have presented a unified system based on a deep neural network, and jointly trained with many NLP tasks, such as: POS tagging, Semantic Role Labeling and Named Entity Recognition. Their model is stored in a matrix M 2 R d⇤|D| , where D represents the dictionary of all unique words in the training data, and each word in D is embedded into a d-dimensional vector. The sentences are represented using the embeddings of their forming words. A similar idea was independently proposed and used by Turian et al. [START_REF] Turian | Word representations: a simple and general method for semi-supervised learning[END_REF].

Mnih and Hinton [START_REF] Hinton | A scalable hierarchical distributed language model[END_REF] have introduced another form to represent words in vector space, named Hierarchical Log-Bilinear Model (HLBL). Like almost all neural language models, the HLBL model is used to represent each word by a real-valued feature vector. HLBL concatenates the (n 1) first embedding words (w 1 ..w n 1 ) and learns a neural linear model to predicate the last word w n .

In Mikolov et al. [START_REF] Mikolov | Linguistic regularities in continuous space word representations[END_REF] a recurrent neural network (RNN) [START_REF] Mikolov | Recurrent neural network based language model[END_REF] is used to build a neural language model. The RNN model encode the context word by word and predict the next word. Afterwards, the weights of the trained network are considered as the word embedding vectors.

Based on the simplified neural language model of Bengio et al. [START_REF] Bengio | A neural probabilistic language model[END_REF], Mikolov et al. [START_REF] Mikolov | Efficient estimation of word representations in vector space[END_REF] [START_REF] Mikolov | Distributed representations of words and phrases and their compositionality[END_REF] presented two other techniques to build a words representations model. In their work, two models are proposed: the continuous bag-of-words (CBOW) model [START_REF] Mikolov | Efficient estimation of word representations in vector space[END_REF], and the skip-gram (SKIP-G) model [START_REF] Mikolov | Distributed representations of words and phrases and their compositionality[END_REF]. The CBOW model, predicts a pivot word according to the context by using a window of contextual words around it. Given a sequence of words S = w 1 , w 2 , ..., w i , the CBOW model learns to predict all words w k from their surrounding words (w k l , ..., w k 1 , w k+1 , ..., w k+l ). The second model, SKIP-G, predicts surrounding words of the current pivot word w k [START_REF] Mikolov | Distributed representations of words and phrases and their compositionality[END_REF].

Pennington et al. [START_REF] Pennington | Glove: Global vectors for word representation[END_REF] proposed a Global Vectors (GloVe) model to representing words in vector space. GloVe model builds a co-occurrence matrix M using the global statistics of word-word co-occurrence. Afterwards, the matrix M is used to estimate the probability of word w i to appear in the context of another word w j , this probability P (i/j) represents the relationship between words.

In a comparative study conducted by Mikolov et al. [START_REF] Mikolov | Efficient estimation of word representations in vector space[END_REF] all the methods [START_REF] Collobert | A unified architecture for natural language processing: Deep neural networks with multitask learning[END_REF], [START_REF] Turian | Word representations: a simple and general method for semi-supervised learning[END_REF], [START_REF] Hinton | A scalable hierarchical distributed language model[END_REF], [START_REF] Mikolov | Linguistic regularities in continuous space word representations[END_REF], [START_REF] Mikolov | Efficient estimation of word representations in vector space[END_REF] and [START_REF] Mikolov | Distributed representations of words and phrases and their compositionality[END_REF] have been evaluated and compared, and they show that CBOW [START_REF] Mikolov | Efficient estimation of word representations in vector space[END_REF] and SKIP-G [START_REF] Mikolov | Distributed representations of words and phrases and their compositionality[END_REF] models are significantly faster to train with better accuracy. For this reason, we have used the CBOW word representations for Arabic model, proposed by Zahran et al. [START_REF] Zahran | Word representations in vector space and their applications for arabic[END_REF]. In order to train this model, they have used a large collection from different sources counting more than 5.8 billion words 2 .

In the Arabic CBOW model [START_REF] Zahran | Word representations in vector space and their applications for arabic[END_REF] each word w is represented by a vector v of ddimension. The similarity between two words w i and w j (e.g. synonyms, singular, plural, feminization or closely related semantically) is obtained by comparing their vector representations v i and v j respectively [START_REF] Mikolov | Efficient estimation of word representations in vector space[END_REF]. This similarity can be evaluated using the Cosine similarity, Euclidean distance, Manhattan distance or any other similarity measure functions. For example, let " ⇣ È™"Am . à '@" (university), "ZAÇ÷oe@" (evening) and " ⇣ ÈJ ⌦ aeÀ@" (faculty) be three words. The similarity between them is measured by computing the cosine similarity between their vector as follows:

Sim(ZAÇ÷oe@, ⇣ È™"Am . à '@) = Cos(v(ZAÇ÷oe@), v( ⇣ È™"Am . à '@)) = 0.13

Sim( ⇣ ÈJ ⌦ aeÀ@, ⇣ È™"Am . Ã '@) = Cos(v( ⇣ ÈJ ⌦ aeÀ@), v( ⇣ È™"Am . Ã '@)) = 0.72

That means that, the words " ⇣ ÈJ ⌦ aeÀ@" (faculty) and " ⇣ È™"Am . à '@" (university) are semantically closer than "ZAÇ÷oe@ " (evening) and " ⇣ È™"Am . à '@" (university). In the following, we exploit this property to measure the semantic similarity at sentence level.

Proposed Methods

In this section, we present our two proposed methods for Arabic-English cross-language sentence similarity. These methods use Machine Translation-Based Model, followed by a monolingual semantic similarity analysis based on word embedding. They consist of three steps, including translation, preprocessing and similarity score attribution. First, MT is used to translate English sentences into Arabic. Afterwards, our two word embedding-based methods are employed to measure the semantic similarity of Arabic sentences. In the first one, we propose to use the words alignment technique proposed by Sulatan et al. [START_REF] Sultan | Dls@ cu: Sentence similarity from word alignment and semantic vector composition[END_REF] with the words weighting methods of Nagoudi and Schwab [START_REF] Nagoudi | Proceedings of the Third Arabic Natural Language Processing Workshop[END_REF], we call this method Weighting Aligned Words (W-AW). The second generate a Bag-of-Words for the aligned words to construct a vector representation of each sentence. Then the similarity is obtained by comparing the two sentence vectors, we name this method Bag-of-Words Alignment (BoW-A). Fig. 2 gives an overview of the proposed methods. Let S E = w e1 , w e2 , ..., w ei and S A = w a1 , w a2 , ..., w aj be an English and Arabic sentence, and their word vectors are (v e1 , v e2 , ..., v ei ) and (v a1 , v a2 , ..., v aj ) respectively. The semantic similarity between S E and S A is computed in three steps: translation, preprocessing and a monolingual similarity score attribution.

1) Translation: in this step, we used Google Translate API 3 to translate English sentences into Arabic language, we denote the translated sentence S E 0 . By this transla-tion, the problem is reduced into a mono-lingual semantic similarity one.

2) Preprocessing : in order to normalize the sentences for the similarity evaluation step, a set of preprocessing are performed:

-Tokenization: input sentences are broken up into words; -Removing punctuation marks, diacritics, and non alphanumeric characters;

-Normalizing @ , @ , @ to @ and ⇣ Ë to Ë , as in the Arabic CBOW model [START_REF] Zahran | Word representations in vector space and their applications for arabic[END_REF]; -Replacing final ¯followed by Z by ¯.

At this point we should mention that we will not remove the stop words because they can affect the similarity score, For example: SE ="Joseph went to university" and SA = " ⇣ È™"Am . à '@ ˙Õ@ I . Î YK ⌦ 'À ≠ÉÒK ⌦ " (Joseph does not go to university). If we remove the words 'À , ˙Õ@ and to as a stop words, both sentences become similar, whereas they have contradictory meanings.

3) Sentences similarity we propose two methods for measuring the semantic similarity between S E 0 and S A : Weighting Aligned Words Method (W-AW) and Bagof-Words Alignment Method (BoW-A). In the following, we develop our proposed methods, and we provide for each one how the semantic similarity is measured.

Weighting Aligned Words Method (W-AW)

A simple way to compare the translated sentence S E 0 and the Arabic one S A is by summing their words vectors [START_REF] Nagoudi | Proceedings of the Third Arabic Natural Language Processing Workshop[END_REF]. Then, the similarity is obtained by calculating the Cosine similarity Cos(V E 0 ,V A ), where: (

V E 0 = P i k=1 v e 0 k V A = P j k=1 v a k
For example, let S E and S A be two sentences:

S E ="Joseph went to college".

S A = " ⇣ È™"Aj . À A´QÂÑ" ˙Ê î÷fl ⌦ ≠ÉÒK ⌦ " (Joseph goes quickly to university).

Step 1: Translation In this step Google Translate API is used to translate the English sentence S E into Arabic S E 0 = " ⇣ ÈJ ⌦ aeÀ@ ˙Õ@ ≠ÉÒK ⌦ I . Î X".

Step 2: Sum of the word vectors

V E 0 = V ( ⇣ ÈJ ⌦ aeÀ@) + V (˙Õ@ ) + V ( ≠ÉÒK ⌦ ) + V (I . Î X) VA = V ( ⇣ È™"Aj . À) + V (A´QÂÑ") + V (˙Ê î÷fl ⌦) + V ( ≠ÉÒK ⌦ )
Step 3: Similarity Score The similarity between S E 0 and S A is obtained by calculating the cosine similarity between the sentence vectors V E 0 and V A as follows:

Sim(S E , S A ) = Sim(S E 0 , S A ) = Cos(V E 0 , V A ) = 0.71
In order to improve the similarity results, we have used the words alignment method presented by Sultan et al. [START_REF] Sultan | Dls@ cu: Sentence similarity from word alignment and semantic vector composition[END_REF], with the difference that we align the words based on their semantic similarity in the word embedding model, and not in a dictionary. We assume also that all words don't have the same importance for the meaning of the sentences.

For that, we use three weighting functions (idf , pos and idf -pos) proposed by Nagoudi and Schwab in [START_REF] Nagoudi | Proceedings of the Third Arabic Natural Language Processing Workshop[END_REF] for weighting the aligned words. Finally, the similarity between S E 0 and S A is calculated as follows:

Sim(S E 0 , S A ) = 1 2 0 @ P w2S E 0 W T (w) ⇤ BM (w, S A ) P w2S E 0 W T (w) + P w2S A W T (w) ⇤ BM (w, S E 0 ) P w2S A W T (w) 1 A (1)
where W T (w) is the function which return the weight of the word w. W T uses three weighting methods: idf , pos and a mix of both. The BM (w, S k ) function represent the Best Match score between w and all words in the sentence S k . Therefore, BM function aligns words based on their semantic similarity included in the word embedding model. The function BM is defined as:

BM (w, S k ) = Max{Cos(v, v k ), w k 2 S k } (2)
For example, let us continue with the same example above, the similarity between S E 0 and S A is obtained in four steps as follows:

Step 1: POS Tagging Firstly, the POS tagger of Gahbiche-Braham et al. [START_REF] Gahbiche-Braham | Joint segmentation and pos tagging for arabic using a crf-based classifier[END_REF] is used to predict the part-ofspeech tag of each word w k in S k . ⇢ P os tag(S E 0 ) = verb noun prop noun P os tag(S A ) = noun prop verb adj noun Step 2: IDF & POS Weighting For weighting the descriptive aligned words, we retrieve for each word w k in the S k its IDF weight idf (w k ), we also use the POS weights proposed in [START_REF] Nagoudi | Proceedings of the Third Arabic Natural Language Processing Workshop[END_REF].

Step 3: Words Alignment In this step, we align words that have similar meaning in both sentences. For that, we compute the similarity between each word in S E 0 and the semantically closest word in S A by using the BM function, e.g BM (˙⌦Ê î÷fl ⌦,

S E 0 ) = Max{Cos(˙⌦Ê î÷fl ⌦,v k ), w k 2 SA} = Cos(v(˙⌦Ê î÷fl ⌦), v(I . Î X)) = 0.85
Step 4: Calculate the similarity The similarity between S E 0 and S A is obtained by using the formula (1), which gives us : Sim(S E 0 , S A ) = 0.82.

Bag-of-Words Alignment Method (BoW-A)

Among the advantages of word embedding is that it allows to retrieve a list of words that are used in the same contexts with respect to a given word w [START_REF] Ganguly | Word embedding based generalized language model for information retrieval[END_REF]. We named this list of words the k-closest words to w. For example, Table 1 shows the 10-closest words of ⇣ È™"Am . Ã '@ and ⇣ ÈJ ⌦ aeÀ@ in the Arabic CBOW model.

BoW( ⇣ È™"Am . à '@) BoW( ⇣ ÈJ ⌦ aeÀ@) ⇣ È™"Am . à 'AK . , ⇣ ÈJ ⌦ aeÀ@, ⇣ È™"Aj . À, ⇣ HA™"Am . à '@, A J ⇣ J™"Ag . , ⇣ ÈJ ⌦ ÷fl ⌦XAøB@, ⇣ È™"Ag . , ⇣ ËXA"™À@, ⇣ HA™"Am . à '@, ⇣ È™"Am . à '@ -Qk A J ⇣ ⌧J ⌦ ø, I . ¢À@ ⇣ ÈJ ⌦ ø, ⇣ È™"Am . à '@, ⇣ ÈJ ⌦ ÷fl ⌦XAøB@, ⇣ È™"Aj . À, ⇣ È™"Ag . , ⇣ HA™"Am . à '@, ⇣ È™"Aj . À, ⇣ ËXA"™À@, ⇣ È™"Am . à '@ ⇣ HAJ ⌦ ø

Table 1: 10-closest words of ⇣ È™"Am . Ã '@ and ⇣ ÈJ ⌦ aeÀ@.

We used this property to evaluate the degree of semantic similarity between S E 0 and S A , we first proceeded to construct a representation vector RV for each sentence. Let RV E 0 and RV A be the representation vectors of S E 0 and S A respectively, the size of each vector is the number of words in its corresponding sentence. The value of an entry in the representation vector, is determined as follows:

1. For each word w we retrieve its aligned word w 0 in the other sentence by using BM function defined by formula (2). 2. We use the embedding model to construct for both w and w 0 their Bag-of-Words BoW w and BoW w 0 . The BoW w (BoW w 0 ) contains the k-closest words to w (w 0 ) in the embedding model. 3. We compute the Jaccard similarity between BoW w and BoW w 0 :

Jacc(BoWw, BoW w 0 ) = BoWw \ BoW w 0 BoWw [ BoW w 0
4. The value of the entry RV [w] is set to Jacc(BoW w , BoW w 0 ). 5. This process is applied for all words in both sentences to build RV E 0 and RV A . 6. Finally, the similarity between S E 0 and S A is obtained by:

Sim(S E 0 , S A ) = 1 2 0 @ P w2S E 0 W T (w) ⇤ RV [w] P w2S E 0 W T (w) + P w2S A W T (w) ⇤ RV [w 0 ] P w2S A W T (w) 1 A (3)

Experiments and Results

In order to evaluate our systems and monitor their performances, we have used four datasets drawn from the STS shared task SemEval-2017 (Task1: STS Cross-lingual Arabic-English) 4 [8], with a total of 2412 pairs of sentences. The sentence pairs have been manually labeled by five annotators, and the similarity score is the mean of the five annotators' judgments. This score is a float number between "0" (indicating that the meaning of sentences are completely independent) to "5" (indicating meaning equivalence). More information about the datasets used is listed in Table 2.

Dataset

Experimental Results

We investigated the performance of both Weighting Aligned Words (W-AW) and Alignment Bag-of-Words (A-BoW) systems with three weighting functions: IDF, POS and mix of both. In addition, for the A-BoW method, we have used four different values of These results indicate that when the IDF weighting method is used the mean correlation rate does not fall below 70% in all tested methods. When applying the POS and mixed weighting, the correlation rate of IDF weighting is outperformed in both methods A-AW and A-BoW with a mean of +2.35% and +3.91% respectively. Interestingly, increasing the parameter k to generate the k-closest words in the A-BoW method, leads each time to an enhancement in the correlation rate. For instance, the use of 15-closest words outperforms the 5-closest system by +2.01% of correlation in average. However, when k is raised to 20, the mean correlation rate gets a bit lower. This is due to the rise of the number of words with different meaning in the BoW.

k
From the above results, we can see that the estimated similarity provided by our approches is fairly consistent with human judgments. However, the correlation is not good enough when two sentences share nearly the same words, but with a totally different meaning, for example: "H . A¢ m à '@ •K . Q' ´ •´AK . A ⇣ Jª Y™É @ Q ⇣ AEK ⌦ " and (Saad reads a book about Omar Ibn Al-Khattab) "H . A¢ m à '@ •K . Q"™À AK . A ⇣ Jª Q ⇣ AEK ⌦ Y™É" (Saad a book Omar Ibn Al-Khattab). In this example, the sentences share the same vectors, POS and weights. This fact leads to a high correlation score, which is not the case. This issue is left for future work.

Comparison with SemEval-2017 Winners

We compared our optimal results with the three best systems proposed in SemEval-2017 Arabic-English cross-lingual evaluation task [START_REF] Cer | Semeval-2017 task 1: Semantic textual similarity multilingual and crosslingual focused evaluation[END_REF] (ECNU [START_REF] Tian | proceedings of the 11th international workshop on semantic evaluation[END_REF], BIT [START_REF] Wu | proceedings of the 11th international workshop on semantic evalua-tion (semeval 2017)[END_REF] and HCTI [START_REF] Shao | proceedings of the 11th international workshop on semantic evalua-tion[END_REF]) and the baseline system [START_REF] Cer | Semeval-2017 task 1: Semantic textual similarity multilingual and crosslingual focused evaluation[END_REF]. In this evaluation, ECNU obtained the best performance with a correlation score of 74.93%, followed by BIT and HCTI with 70.07% and 68.36% respectively. Table 4 shows a comparison of our best results with those obtained by the three systems were tested on the STS Evaluation Data5 . The observed results indicate that our mixed weighted method with k = 15 is the best performing method with a correlation rate of 77.39%. The W-BoW-IDF-POS (k = 15) method yields a gain of +9.03%, +7.32% and +2.46% on the correlation rate compared with ECNU, BIT and HCTI respectively.

Methods

Conclusion and Future Work

In this paper, we have presented two methods for measuring the semantic relations between Arabic-English cross-language sentences using Machine Translation (MT) and word embedding representations. The main idea is based on the usage of semantic properties of words included in the word-embedding model. In order to make further progress in the analysis of the semantic sentence similarity, we have used a combiof words IDF and POS weighting to support the identification of words that are most descriptive in each sentence. Additionally, we evaluated our proposals on the four datasets of the STS shared task SemEval-2017. In the experiments we have shown how the Bag-of-words method clearly enhanced the correlation results. The performance of our proposed methods was confirmed through the Pearson correlation between our assigned semantic similarity scores and human judgments. In fact, we reached the best correlation rate compared to all the participating systems in STS Arabic-English cross-language subtask of SemEval-2017. As future work, we are going to combine these methods with those of other classical techniques in NLP field, including word sense disambiguation, linguistic resources and document fingerprint in order to make more improvement in the cross-language plagiarism detection.

Fig. 2 :

 2 Fig. 2: Overview of the proposed methods

Table 2 :

 2 Arabic-English Evaluation Sets.

		Source	Pairs
	MSRvid	Microsoft Research Video Description Corpus	736
	MSRpar	Microsoft Research Paraphrase Corpus	1020
	SMTeuroparl	WMT2008 develoment dataset	406
	STS Evaluation Data SNLI Corpus	250

Table 3 :

 3 to generate the 5-closest, 10-closest, 15-closest and 20-closest words. Afterwards, in order to evaluate the accuracy of each method, we calculate the Pearson correlation between our assigned semantic similarity scores and human judgments on the SemEval STS task datasets. Table3reports the results of the proposed methods. Our methods Vs human judgments

	Method	MSRvid MSRpar SMTeuro.	STS Eval. Mean
	W-AW-IDF	0.6895	0.7019	0.7274	0.6951	0.7034
	W-AW-POS W-AW-IDF-POS 0.7015 0.6924	0.7402 0.7385	0.7478 0.7512	0.7205 0.7375	0.7252 0.7321
			k = 5
	A-BoW-IDF	0.6863	0.7119	0.7174	0.6881	0.7009
	A-BoW-POS A-BoW-IDF-POS 0.7074 0.6933	0.7349 0.7365	0.7364 0.7482	0.7187 0.7362	0.7218 0.7320
			k = 10
	A-BoW-IDF	0.6879	0.7131	0.7291	0.7114	0.7103
	A-BoW-POS A-BoW-IDF-POS 0.7216 0.7084	0.7437 0.7418	0.7514 0.7603	0.7305 0.7565	0.7335 0.7450
			k = 15
	A-BoW-IDF	0.6954	0.7089	0.7284	0.7254	0.7145
	A-BoW-POS A-BoW-IDF-POS 0.7575 0.7124	0.7402 0.7485	0.7578 0.7672	0.7391 0.7739	0.7398 0.7603
			k = 20
	A-BoW-IDF	0.6912	0.7055	0.7283	0.7254	0.7244
	A-BoW-POS A-BoW-IDF-POS 0.7525 0.7254	0.7382 0.7477	0.7514 0.7689	0.7351 0.7613	0.7351 0.7576

Table 4 :

 4 Comparison of the correlation results with three best systems in SemEval-2017.

		STS Eval.
	W-BoW-IDF-POS (k = 15) 77.39%
	ECNU	74.93 %
	W-AW-IDF-POS	73.75%
	BIT	70.07 %
	HCTI	68.36%
	Cosine baseline	51.55 %

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