=Paper=
{{Paper
|id=Vol-1398/SocInf2015_Paper4
|storemode=property
|title=Influential Analysis in Micro Scholar Social Networks
|pdfUrl=https://ceur-ws.org/Vol-1398/SocInf2015_Paper4.pdf
|volume=Vol-1398
|dblpUrl=https://dblp.org/rec/conf/ijcai/WeigangDSL15
}}
==Influential Analysis in Micro Scholar Social Networks==
Proceedings of the 1st International Workshop on Social Influence Analysis (SocInf 2015) July 27th, 2015 - Buenos Aires, Argentina Influential Analysis in Micro Scholar Social Networks Li Weigang1,2, Icaro Araújo Dantas1, Ahmed Abdelfattah Saleh2, Daniel L. Li3 1 TransLab, Department of Computer Science, University of Brasilia, Brasilia, Brazil 2 PPMEC, Department of Mechanical Engineering, University of Brasilia, Brasilia, Brazil 3 Coleman Research, Raleigh, North Carolina-NC, USA weigang@unb.br, icaro.a.dantas@gmail.com, ahmdsalh@yahoo.com, daniel.lezhi.br@gmail.com Abstract In Google Scholar, the most cited paper is “A short history of SHELX” [Sheldrick, 2007] with 49,792 citations. The Scholar citation is a basic activity in scientific community. Some academic search engines have authors who cited this paper have composed a special society been developed in Web such as Google Scholar and or a network. Understanding the relations in this society is Microsoft Academic Search. Efficient flexible valuable to the researchers. querying method is essential for researchers to ef- In this massive academic network, efficient querying fectively follow trends within related topics of their models of academic search engines or databases is crucial for research field. In this paper, we propose a procedure a researcher to conduct his research while following up the to construct Micro Scholar Social Networks (MSSN) development trends in a specific research topic of particular from Google Scholar and then develop a querying scientific field. and ranking method to find the influential re- There are two problems that should be deeply studied: 1) searchers or articles in MSSN. An extension to the developing efficient method and system (in Web tool level) Follow Model (Extended Follow Model) is pro- to construct Micro Scholar Social Network (MSSN) for an posed in this paper and applied to describe the pa- especial topic or field from large scholar social networks, per-citation and author-follow relationships. It is such as Google Scholar, Microsoft Academic Search, Web of also coupled with different ranking algorithms, Science or others; 2) developing efficient mining algorithms namely, PageRank, AuthorRank and InventorRank to analyze this MSSN for scholar´s diversity objectives. to study a MSSN in Air Traffic Management. The In literature, some research developed the mining methods case study shows that Extended Follow Model is of heterogeneous information networks [Sun et al. 2012]. robust and efficient for ranking and mining a het- Ahmedi et al. focused on the study of the property of the erogeneous academic network. In spite the fact that Co-authorship Networks [Ahmedi et al., 2011]. study was done on Google Scholar, but the pro- In recent years, many researches proposed solutions to posed data mining method is applicable for other these problems. Liu et al. [2005] demonstrated AuthorRank. academic search engines. AMiner has been developed by [Tang et al., 2008] as a scholar platform with the database and search interface. 1 Introduction W-entropy was proposed to measure the influence of the With the development of Internet technology and applica- members from social networks [Weigang et al., 2011]. Sandes et al. [2012] introduced the concept of Follow Model tions, there are at least 114 million English-language schol- for the development of advanced queries on social networks. arly documents accessible on the Web [Khabsa and Giles, Du et al. [2015] demonstrated the way of analyzing im- 2014]. The term “scholarly documents” here refers to journal portance of nodes in heterogeneous networks. and conference papers, books, dissertations and theses, In this paper, Extended Follow Model (EMF), an extension technical reports and working papers. The size of scholarly to the Follow Model presented by [Sandes et al, 2012], is documents accessible through the web differs from one proposed. EMF is applied to describe the paper-citation and academic search engine to the other; Google Scholar1, for author-follow relationships. It is also coupled with different example, comprises nearly 100 million scholarly documents ranking algorithms, namely, PageRank, AuthorRank and and also available advanced search for general consulting. InventorRank to study a MSSN in Air Traffic Management. The case study shows that Extended Follow Model is robust and efficient for ranking and mining a heterogeneous aca- demic network. In spite the fact that the MSSN used in this 1 http://scholar.google.com/ study was constructed using Google Scholar, but the study is Copyright © 2015 for the individual papers by the papers' authors. applicable, as well, for other academic search engines. Copying permitted for private and academic purposes. This volume is published and copyrighted by its editors. 22 Proceedings of the 1st International Workshop on Social Influence Analysis (SocInf 2015) July 27th, 2015 - Buenos Aires, Argentina 2 Micro Scholar Social Networks (MSSN) relevant to their paper. As such, the follow relation, as per the Follow Model introduced by [Sandes et al, 2012], can be used This section introduces the concept of Micro Scholar Social to describe the citation relation between authors. Networks (MSSN) and explains its basic elements and rela- • Followee (Citation relation): Citations of a paper p are tions using Google Scholar as an example. In a MSSN, those papers that were cited by p. The authors of these authors and publications are considered the main objects. However, in addition to authors, there are also editor of the papers are followee of the authors of p. journal, editor of the book, conference chairs. As for publi- • Follower (Cited In relation): Cited Ins of a paper p are cations, there are journal papers, conference papers, books, those papers that cited p. The authors of these papers are book chapters, reports and others. In this study, we use paper followers of the author of paper p. to refer to all different types of publications, and author for • R-Friends (Both-cited relation): Two papers a and b are all contributors. The specification of other objects will be considered Both-Cited, in the case that paper a cites b and considered in our future data mining studies. paper b cites a. The authors of those two papers are The “Micro Scholar” term refers to a specific research R-Friends. field, while “Social Network” term refers to the network • Self-Following (Self-Citation): If an author has cited one constructed from the relations between papers and authors of of his own papers. that field. Figure 1 shows the MSSN constructed from 165 Co-author relation between authors papers and 249 authors of the “Air Traffic Management Another important relation among authors is that of (ATM)” research field. As seen in figure 1, MSSN-ATM is co-authorship. Where, for any particular paper, there are constructed of directed graphs, whose vertices are papers one or more authors. The relationship among those authors (sub-graph a) or authors (sub-graph b) while the edges rep- can be referred to as co-author. An author may be a resent the relations among those elements. co-author for several authors in one or more papers. This paper presents a weighing formula to assign a representitve weight for each author depending on the order of authorship of different papers. 2.2 Types of MSSN Scientific papers are characterized by multiple attributes (e.g. authors, venue, publish time, editor of the journal, editor of the book, conference chairs, etc.) in addition various relations among these attributes. As such, MSSN is considered a kind of heterogeneous information network that contains multiple Figure 1: ATM-MSSN of Google Scholar; a) 165 papers and types of elements and links [Sun et al., 2012], [Kim and their citations; b) Follow relations of 249 authors. Leskovec, 2012]. According to the nature of the elements used to construct a 2.1 Elements and Relations in MSSN Micro Scholar Social Networks, MSSN’s can be divided into two types; i) Homogenous MSSN, with vertices (nodes) The basic elements in MSSN are papers, authors, venue and created using the same elements (i.e. papers or authors); and publishers. This paper focuses on the information related to ii) Heterogeneous MSSN, where the networks vertices in- paper and author. Citation and co-authoring are the core clude different classes of elements (i.e. papers and authors) relations between papers and authors. As such, a MSSN is with their subsequent relations. constructed using the citation relations among papers and authors, in addition to the co-author relations among different 2.2.1 Constructing Homogenous MSSN authors. These relations among MSSN elements can be Regarding the relations in MSSN, there are citation relations explained as follows: (citation, cited in and both cited) between papers, as well as Relations between papers co-author relations and Follow relations (followee, follower, • Citation relation: Citations of a paper p are those papers r-friends) between authors. These relations form three sets of that were cited by p. homogenous MSSN’s. • Cited In relation: Cited Ins of a paper p are those papers A. ATM-MSSN-Papers that cited p. Figure 1(a) shows a MSSN of Air Traffic Management • Both-cited relation: Two papers a and b are considered research topic, which is represented by a graph whose ver- Both-Cited, in the case that paper a cites b and paper b tices are papers and the citation relation is its edges. The data cites a. reflected in this graph was collected from Google Scholar in Follow relation between authors January 26, 2015. Citation relation can be extended to describe the relation To create the graph, a citation relation matrix Pc is intro- among authors. Where, when a paper cites another paper, in duced. Pc is a square matrix of size (N × N), where N is the actuality, authors are simply citing authors with prior studies total number of papers in the ATM-MSSN. pcij is an element 23 Proceedings of the 1st International Workshop on Social Influence Analysis (SocInf 2015) July 27th, 2015 - Buenos Aires, Argentina of the Pc matrix, with i, j= 1,2,…N. As such, if a paper i cited a matrix of size (M × N), with M is the total number of au- a paper j then pcij = 1. thors in the model, while N is the total number of papers. The matrix element paij represents the weight of author i in B. ATM-MSSN-Authors writing the paper j. In other words, if a paper j has only one Figure 1(b) shows a graph with follow relations among 249 author I then paij = 1. While for a paper i written by more than authors. A close relation can be observed between the two one author, then the value of paij depends on the order of subfigures, where, subfigure 1(b) is based on 1(a), the only authors who wrote that paper [Du et al., 2015], the equation is difference is that one paper can be written by more than one modified as author. 1 1 The author relation matrix A is introduced to create this 1 1 graph. A is a square matrix of size (M × M), where M is the 1 1 total number of authors in the ATM-MSSN. aij is an element of the A matrix, with i, j= 1,2,…M. such, aij represents the number of times an author i follows an author j. B. ATM-MSSN-Author-CoAuthor graph C. ATM-MSSN-CoAuthors Other type of heterogonous graphs is that constructed using Figure 2(a) shows the co-author relations among 249 authors. the same class element (e.g. authors) and then connected by An author can be a co-author with more than one author. different types of relations (e.g. follow and co-author rela- The co-author relation matrix Ac is introduced to create tions). this graph. Ac is a square matrix of size (M × M), where M is the total number of authors in the ATM-SSN. acij is an ele- Therefore, constructing MSSN’s graphs is the core step in ment of the matrix Ac, with i, j= 1,2,…M. such, acij repre- building an efficient data-mining model that is used to per- sents the number of papers in which authors i and j are form complex analytical queries. As such, suitable hetero- co-authors. geneous and/or homogenous graph representation is selected to achieve the intended goal of the mining study. These graphs could be extended to include various attributes (con- ferences, journals, publishers, etc.) in order to develop a data-mining model that is capable of analyzing the relations among these attributes. 3 Extended Follow Model and Querying In this section we extend the Follow Model, introduced by [Sandes et al. 2012], as the best way to model MSSN’s and Figure 2: a) Homogenous ATM-MSSN-CoAuthors; b) perform effective queries. In addition, PageRank and other Heterogenous ATM-MSSN. ranking methods can be coupled with Extended Follow Model (EFM) to perform advanced queries. 2.2.2. Constructing Heterogeneous MSSN Heterogeneous MSSN is formed of multiple elements and/or 3.1 Extended Follow Model (EFM) relations. As such, a heterogeneous MSSN can be con- MSSN can be best described in the form of directed graph G structed using multiple elements (e.g. papers and authors) = (V, E) where the vertices set V represents the papers and/or and connected using a particular relationship and/or multiple authors, while the directed edges E: V×V represents the more types of relations; E can be noted as Ea, Ep or ∪ ! . relations for the same element class (e.g. co-author and relations between them. For heterogeneous MSSN, there are follow relations for authors). A. ATM-MSSN-Author-Paper graph The author follow relation (v, u) ∈ Ea means that author v Figure 2(b) shows ATM-MSSN, which is a heterogeneous follows author u, and the graph Ga = (Va, Ea) presents the MSSN constructed using two classes of elements, papers and author relationship. While, (a, b) ∈ Ep means that paper a authors. Where, authors’ nodes are represented by red circles while the papers’ nodes are represented by blue triangles. cites paper b, and the graph Gp = (Vp, Ep) presents the paper The citation relation connects the paper nodes, while follow relationship. relation connects the authors. The two classes of nodes are As such, the Extended Follow Model (EFM) can effi- then connected together using weighted co-authorship rela- ciently describe the relations between the MSSN classes as tion, where every author-paper edge has a weight that reflects mentioned in section 2.1. Where two authors can be related the level of involvement (order) of this author in the au- as either; followee, follower or r-friends while two papers are thorship of that paper as seen in equation 1. According to related as cited (followee), cited in (follower) or both-cited figure 2(b), a matrix PA can be used to present the relations (r-friends). between authors and papers in the ATM-MSSN model. PA is Using these relations, one can construct data subsets for 24 Proceedings of the 1st International Workshop on Social Influence Analysis (SocInf 2015) July 27th, 2015 - Buenos Aires, Argentina big data querying. These data subsets can be extracted using • An author of a paper p may be interested in the papers used, * ( , where P(p) is the set of all papers the following functions: that cited his paper. In this case Follow model can be fout(u)={v|(u,v)∈Ea}, (2) where, fout(u) is the followee function to present the subset, that cited the paper p (Cited Ins). → Vout, of all followees, v, of author u, Va Vout, Va⊂V; |fout(u)| • The same author may be interested in listing authors who + ( , where A(p) is the set of authors that cites follow him, therefore according to follow model, of author u; "#$ &={p(v)|(u,v)∈Ea}, p(v) is a value of the % is the number of the elements (authors) in the followee subset paper p (i.e. followers of the author). author etc. "#$ &={w(v)|(u,v)∈Ea}, w(v) is a weight value author v, such as the order in the subset or h-index of the ' • One of many other interesting queries in the same con- text is obtaining the list of papers cited by those papers of the link between the authors u and v, such as the number of that cited p, or in other words, the list of followees of the query using + "#$ ( citations etc. author’s followers A(p). Follow model can simplify this fin(u)={v|(v,u)∈Ea}, (3) papers that cites a particular paper (cited by his paper where, fin(u) is the follower function to present the subset, • In addition an author may be interested in the set of → Vin, of all followers, v, of author u, Va Vin, Va⊂V; |fin(u)| is as well) in addition to his paper p. As such, f(pi) = fin(p) author; ( &={p(v)|(v,u)∈Ea}, p(v) is a value of the author % the number of the elements (authors) in the follower subset of ∩ paper p in addition to . fin(pi), where P(pi) is the set of all papers that cited his (' &={w(v)|(u,v)∈Ea}, w(v) is a weight value of the link Using Follow model, * "#$ , where P(p) is the v, such as the order in the subset or h-index of the author etc. • Other users may be interested in the citations of paper p. between the authors u and v, such as the number of citations. set of the papers that were cited by p. ∩ fr(u)=fout(u) fin(u), (4) • Other queries include: finding out the set of top-x (x may where, fr(u)is the r-friend function to present the subset, be 5 or more) papers, in terms of number of Cited Ins, for → Va, of all r-friends of author u, Va Vr, Va⊂V. |fr(u)| is the query as * ( "#$ , , where fout(p) is a func- the papers cited by p. Follow model can present this author; ) &={p(.)}, p(.) is a value of the r-friends of author % paper p; ( -.,is a function generating the top 5 pa- number of the elements (authors) in the r-friend subset of tion containing the set of papers (Pc) that were cited by )' &={w(.)}, w(.) is a weight value of the link between the u, such as the order in the subset or h-index of the author etc. pers, cited papers of the set Pc, that have the highest number of Cited-Ins. author u and his f-friends, such as the number of co-author, • Also, finding out the set of top-x papers, in terms of the etc. influence of the paper or the authors, for the papers that present this query as * "#$ ( /0 , With these basic definitions, EFM has both numeric |f(.)| were cited by the papers that cited p. Follow model can where( is a function containing the set of papers and symbolic f(.) representations for more sophisticated (Pc) that cited paper p; "#$ -./0 is a function relationships between users. The Follow Model is also characterized by three properties: reverse relationship, compositionality, and extensibility generatingthe top 10 papers, that were cited by papers of [Sandes et al. 2012, Weigang et al., 2014]. Joining functions the set Pc, that have the highest influence. Different ranking algorithms, explained in the following section, allow us to create many other relationship functions. For can be used to determine the influence of papers and ( & represents the followers of followers of u; "#$ & example: finfout(u) represents the followers of followees of u; authors. represents the followees of followees of u; ) & represents 4 Influential Scholar Ranking Models the r-friends of r-friends of u. Ranking algorithms can be used to find the influential In this research, beside EFM is applied as a querying scholars in a MSSN. This section presents three ranking method for MSSN-AUTHOR, it is also used in methods: PageRank, AuthorRank and InventorRank. All MSSN-PAPER by three functions: 1) fout(p) is a function to these models are presented in the form of Extended Follow present all papers which are cited by paper p; 2) fin(p) is a Model. function to present all the papers which cited the paper p; and 3) fr(p) is a function to present the paper p´s both-cited, which 4.1 PageRank and AuthorRank are papers that cited p and were cited by p. PageRank [Brin and Page, 1998] can be presented in the form 4( % 3.2 Querying Google Scholar using Follow Model of EFM as follows: *1 1 – 3 8 |"#$ 6( 7| EFM can be applied for querying in MSSN from Google (5) Scholar or Microsoft Academic Search to satisfy the needs of users of these academic search engines. For example: 25 Proceedings of the 1st International Workshop on Social Influence Analysis (SocInf 2015) July 27th, 2015 - Buenos Aires, Argentina where, i is an author, ( is the set of the values of all % authors who linked (followed) to i, and 4( is the sum % Note that AuthorRank was not modified to use this tech- of the values in this set. |"#$ 6( 7| is the number of nique due to the fact that this method is restricted to classi- fication of a network that contains only authors. followers of the followee of i. On the other hand, AuthorRank is an indicator of the 5 ATM-MSSN Ranking Case Study impact of an individual author in the network [Liu et al. In this section, the ranking case study in ATM-MSSN is 2005]. This algorithm is considered as an improvement of described in details, to demonstrate how EFM can be coupled PageRank algorithm. Where, weights of nodes represent the with three classification algorithms; PageRank, AuthorRank number of times by which an author was co-author with and InventerRank; to achieve effective querying. It also another. Using EFM, AuthorRank can be represented as demonstrates the application of SJR to obtain influential ' ( follows: rankings. +1 1 – 94 3: ; . 8= % 4"#$ ( ( In figure 2(b), Heterogenous ATM-MSSN includes a total ' (6) of 249 authors and 165 papers. Citation relationships Where, the >A ?@.. ? represents the weights of the followee between the papers (where an article cites others) and of i and >ABCD ?@ ? represents the weights of the followers > between the authors (an author cites / follows others) are illustrated. There is also another kind of relationship between of the followee of i. authors and articles which is defined as the co-authoring relationship. 4.2 InventorRank For all these tests, the parameters of the models are defined parameter d was set at 0.5. For the parameters, αOO , αOQ e αQO , In the study of the data model of the inventor-ranking by the following pattern: For PageRank and AuthorRank, framework, [Du et al. 2015] demonstrates how to perform I and I% were both set as 0.5. The classification values analysis of important nodes in heterogeneous networks. EFM the values were 0.4, 0.4 and 0.2 respectively. The is used to present one of the three rules described by [Du et al. 2015] for determining influential authors based on were all obtained from SJR´s site: co-authorship. Where, highly ranked authors tend to http://www.scimagojr.com/. If there is no journal, it is co-author with other highly ranked authors. The first rule of considered as null classification and does not influence the InventorRank is determined using the following equation: ranking calculation. 1 E F GH46)' . ) . I 7 1 E1 I . |) E|JK 7 % 5.1 Ranking authors and papers without SJR The first result obtained is related to the author´s ranking in where Ri(k) is the rank of author k, fr(k) is the set of the all ATM-MSSN. The ranking results are diferent due to the co-authors of k. See other rules in [Du et al. 2015]. diferent characteristics of each model. From Table 1, it is possible to observe that each profile at 4.3 Adjusting PageRank and Inventor Rank with the top of the ranking reflects the characteristics that most SJR affect the model. Based on the fact that articles are usually published in some Table 1. Author´s Ranking for ATM-MSSN events or journals, González-Pereira [2010] proposes a way to classify the influence of a journal, based on the weight of Ranking AuthorRank InventorRank PageRank citations and eigenvector centrality, in heterogeneous net- 1 J F Butler E Ferons A R Odoni works, this model is called SCImago Journal Rank (SJR). 2 H N Psaraftis L Kang D Trivizas Siebelt et al. [2010] e Macedo et al. [2010] are examples of some researchers that suggest using SJR to calculate the 3 G Roger J P Clarke H N Psaraftis importance of an article. It is suggested that, like Du et al. 4 Dear B Delcairet E P Gilbo [2015] used the classification of journals for classifying authors, it is possible to use periodicals classification as a 5 B G Sokkappa W D Hall Dear mean for calculating journals or authors importance. As such 6 L Gippo H Idris G Roger this paper proposes adding journals weights in the previously 7 M Cini R Bhuva D J Bertsimas defined classification algorithm. Thus, modified equations can be as follows: 8 S S Patterson AR Odoni A Hormann 9 C F Dayl R Hoffman S S Patterson PageRank: SR(i) = PR(i) * SCImago_Rank (8) 10 G Andreatta D J Bertsimas B G Sokkappa 1% M = 1% M * SCImago_Rank InventorRank: (9) Author A R Odoni appears first according to PageRank because his papers have the most citations in ATM-MSSN, at 26 Proceedings of the 1st International Workshop on Social Influence Analysis (SocInf 2015) July 27th, 2015 - Buenos Aires, Argentina a total of 13 citations (followees). E Ferons, best ranked by even published as they were simply graduate dissertations or InventorRank model, co-authored with A R Odoni, B internal reports within the institution. Delcairet, H Idris, J P Clarke, W D Hall e B Delcairet, all Table 3 Top 10 Authors Ranking Considering SJR well ranked authors in ATM-MSSN. This shows that although A R Odoni received many citations, a total of 89 Ranking Name (followers), it was not significant enough to affect his 1 A R Odoni ranking because those that work with him are not the best 2 M O Ball ranked in the network. In case of AuthorRank, J F Butler 3 W D Hall received top ranking because his papers received most of the 4 D J Bertsimas citations from A R Odoni, G Andreatta and B G Sokkapa. 5 E Ferons Table 2, which lists the Top 5 papers by PageRank and 6 R Hoffman InventorRank. For InventorRank, the paper´s ranking is 7 G Lulli affected mostly by the authors’ influence, and vise-vesa. This 8 H Idris correlation is not observed in PageRank. 9 J P Clarke Table 2. Top 5 papers by PageRank and InventorRank 10 G L Nemhauser On the other hand, the InventorRank demonstrates its robustness even with the addition of different features to the network. Its ranking of papers remained consistent and very similar to the first classification in table 2, where SJR was not taken into consideration. Table 4. Top 5 Papers Considering SJR in Ranking 5.2 Ranking authors and papers considering SJR When analyzing the best papers ranked by InventorRank, it is observed that the position of the authors influence dictates 6 Conclusion the paper's ranking. PageRank does not yield similar results This paper presents the construction of Micro Scholar Social and relations, because it is not well structured to evaluate Networks (MSSN) for specific research topic using Google heterogeneous networks. The tests below analyze how these Scholar academic search engine. Extended Follow Model models operate when adding new characteristics to the (EFM) was proposed as a comprehensive way of creating network. efficient data-mining model for querying homogenous and From table 3, it is possible to observe that the heterogeneous MSSNs. By means of the advantages, EFM InventorRank differed in the ranking of a few others, which was coupled with ranking algorithms to achieve a full que- indicates that its results obtained in table 1 may not be rying and ranking models for scholarly documents of Google representative. Table 3 shows that the weight of SJR for the Scholar. journals where E Ferons’ articles were published did not Comparing the results of such algorithms shows that contribute to his rankings. Instead, A R Odoni , M O Ball and InventorRank is a much more robust and accurate model, others are well ranked. especially when considering the amount of information used Comparing Table 2 to Table 4, we observe that PageRank for classification and ranking. Where, InventorRank can be is altered significantly when considering SJR. This was a easily adapted to adding new features to the network, in result of either the quality of the journals where the articles addition to its flexibility resulted from the ability to set the were published, or in some cases where the articles were not 27 Proceedings of the 1st International Workshop on Social Influence Analysis (SocInf 2015) July 27th, 2015 - Buenos Aires, Argentina degree of importance of each term of the algorithm. On the [Macedoa et al., 2010] Luciana G. Macedoa, Mark R. other hand, changes in the network directly affect classifica- Elkinsb, Christopher Mahera, Anne M. Moseleya, Robert tion ability of Pagerank algorithm. D. Herberta, Catherine Sherrington. There was evidence It is worth mentioning that Extended Follow Model pro- of convergent and construct validity of Physiotherapy vides a simple and efficient means for representing several Evidence Database quality scale for physiotherapy trials. existing ranking models. 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