Structural Analysis in Multi-Relational Social Networks

Transcription

1 Singapore Management University

2 Multi-Relational Social Networks Social networks are often multi-relational

3 Multi-Relational Social Networks Social networks are often multi-relational In Facebook, one can write on other s wall poke her friends tag her friends in her own photos

4 Multi-Relational Social Networks Social networks are often multi-relational In Facebook, one can write on other s wall poke her friends tag her friends in her own photos Information is lost if represented by a single relational network as different interactions are treated the same, making them indistinguishable

5 Relations in a Multi-Relational Social Network A multi-relational network allows multiple relations to exist between individuals A relation represents a social connection or a set of interactions of the same kind between two individuals

6 Relations in a Multi-Relational Social Network A multi-relational network allows multiple relations to exist between individuals A relation represents a social connection or a set of interactions of the same kind between two individuals Alice is a friend of Bob on facebook Alice is a classmate of Bob in school The Edge from Alice to Bob Alice wrote on Bob s facebook wall Alice tagged Bob on her facebook photo Alice poked Bob on facebook Saturday Monday Wednesday Sunday

7 Relationships in Multi-Relational Social Networks Each relation, e.g., is-a-friend-of, write-on-wall, poke and tag, defines a single relational network

8 Relationships in Multi-Relational Social Networks Each relation, e.g., is-a-friend-of, write-on-wall, poke and tag, defines a single relational network A multi-relational network can be treated as a merger of multiple single relational networks Alice Bob write on wall poke tag

9 Relationships in Multi-Relational Social Networks Each relation, e.g., is-a-friend-of, write-on-wall, poke and tag, defines a single relational network A multi-relational network can be treated as a merger of multiple single relational networks Alice Bob write on wall poke tag An edge between two nodes in a multi-relational network is called a relationship, which consists of all social connections and interactions between the two individuals

10 In a multi-relational network, each relation suggests different association semantics between two individuals

11 In a multi-relational network, each relation suggests different association semantics between two individuals The interactions occurred between two people largely depend on their positions in the social network and the roles they play

12 In a multi-relational network, each relation suggests different association semantics between two individuals The interactions occurred between two people largely depend on their positions in the social network and the roles they play The position (or social position) refers to a collection of individuals sharing similarity in their relationships; the role (or social role) refers to the relationship between individuals or between positions

13 An Example Alice works in marketing, and she makes use of social networks to promote her products by posting product recommendations on others walls Bob s hobby is photography, and he tags his friends appearing in his photos

14 An Example Alice works in marketing, and she makes use of social networks to promote her products by posting product recommendations on others walls Bob s hobby is photography, and he tags his friends appearing in his photos This explains why Alice performs a lot of write-on-wall interactions, whereas Bob performs a lot of tag interactions

15 An Example Alice works in marketing, and she makes use of social networks to promote her products by posting product recommendations on others walls Bob s hobby is photography, and he tags his friends appearing in his photos This explains why Alice performs a lot of write-on-wall interactions, whereas Bob performs a lot of tag interactions Alice and Bob have marketer and photographer positions respectively in the network due to their distinct relationship compositions with others

16 Our Problem The Problem: Our structural analysis problem on a multi-relational social network is thus to discover groupings of individuals and relationships corresponding to positions and roles respectively

17 Our Problem The Problem: Our structural analysis problem on a multi-relational social network is thus to discover groupings of individuals and relationships corresponding to positions and roles respectively Our Proposed Solution: Generalized Stochastic Blockmodels (GSBM)

18 Comparison with other Blockmodels Blockmodels Binary or Valued Multi- Mixed Stochastic Networks Relational Membership [White 76] Binary [Holland 83] Binary [Fienberg 85] Binary [Wang 87] Binary [Doreian 05] Binary [Žiberna 07] Valued [Airoldi 08] Binary [Gallagher 10] Valued GSBM Valued

19 Modeling Interactions in Social Networks The relationship from node i to node j, Y i,j, is represented by a m-dimensional vector, each dimension represents the count of interactions of the same kind

20 Modeling Interactions in Social Networks The relationship from node i to node j, Y i,j, is represented by a m-dimensional vector, each dimension represents the count of interactions of the same kind The relationship from Alice to Bob: { write-on-wall:2, poke:2, tag:1 }, or (2, 2, 1) if the order of the relations is clear

21 The Generative Model z i j = v Buv z i j = u s k k Y i,j MVPDF s m ( B u,v )

22 MVPois: a MVPDF for Correlated Relations Relations are often correlated We model the correlation using Multivariate Poisson Distribution (MVPois) {W} {P} {T} {W,P} {P,T} {W,T} The probability of the relationship (2, 2, 1) can be obtained by summing up all probabilities of the combination in each row.

23 Experimental Study: Synthetic Data k=4 k=6 k=8 k = 10 k = 12 Vertices Grouped by Ground Truth Positions Vertices in Random Order Vertices Grouped by Predicted Positions using GSBM+mPois Vertices Grouped by Predicted Positions using GSBM+MVPois

24 Experimental Study: IMDb Data Varying Prediction Time Frame with Training Data [03,06] Baseline Precision GSBM Precision Baseline Soft Precision GSBM Soft Precision 0.8 Precision [07,07] [07,08] [07,09] [07,10] [07,11] [07,yy]: Test Data From Year 07 to Year yy

25 Case Study: 73 Movies George Clooney Brad Pitt Matt Damon Bernie Mac Elliott Gould B A Chris Columbus Jon Favreau Ron Howard Doug Liman Christopher Nolan Guy Ritchie Martin Scorsese Steven Soderbergh Steven Spielberg David Yates James Cameron Dan Brown Chris Brigham Jordan Goldberg Kevin Feige C F Daniel Radcliffe Emma Watson Rupert Grint Bonnie Wright Michael Gambon Alan Rickman David Barron Frederic W. Brost David Heyman Gregory Jacobs Lorne Orleans Lionel Wigram D E Tom Hanks Leonardo DiCaprio Russel Crowe Robert Downey Jr. Tom Hardy

26 Conclusion Generalized Stochastic Blockmodels (GSBM) discover structures on multi-relational networks with a given MVPDF. Multivariate Poisson Distribution (MVPois) is proposed to capture the correlation among the relations when modeling multi-relational social networks.