Heterogeneous Networks Jie Tang*, Tiancheng Lou*, and Jon Kleinberg + - PowerPoint PPT Presentation

Inferring Social Ties across Heterogeneous Networks Jie Tang*, Tiancheng Lou*, and Jon Kleinberg + *Tsinghua University + Cornell University 1

Real social networks are complex... • Different social ties have different influence on people – Close friends vs. Acquaintances – Colleagues vs. Family members • However, existing networks (e.g., Facebook and Twitter) are trying to lump everyone into one big network – FB tries to solve this problem via lists/groups – However … • Google+ which circle? Users do not take time to create it. 2

Example 1. Advisor-advisee relationship Arnetminer 3

Example 2. Trustful relationship Adam Adam review trust distrust review Bob Product 1 Bob distrust trust Chris Chris review Danny review Danny Product 2 Epinions 4

Example 3: Friendship in mobile network Friends Other Both in office From Home 08:00 – 18:00 08:40 0.89 0.98 From Office 11:35 0.77 From Office From Office 17:55 15:20 0.70 0.63 0.86 From Outside 21:30 Mobile 5

Inferring Social Ties Across Networks Output: Inferred social ties in Input: Heterogeneous Networks different networks Reviewer network Epinions Adam review Adam review distrust trust Product 1 Bob Bob distrust Chris trust Chris review review Danny Danny Product 2 Knowledge Transfer for Inferring Communication network Social Ties Mobile Both in office From Home Colleague 08:00 – 18:00 08:40 Family From Office Colleague 11:35 From Office From Office 17:55 15:20 Friend Colleague From Outside 21:30 Friend 6

Inferring Social Ties Across Networks Output: Inferred social ties in Input: Heterogeneous Networks different networks Reviewer network Epinions Adam review Adam review distrust trust Product 1 Bob Bob distrust Chris trust Chris review Questions: review Danny Danny Product 2 Knowledge - What are the fundamental forces behind? Transfer for Inferring Communication network Social Ties Mobile - A generalized framework for inferring social ties? Both in office - How to connect the different networks? From Home Colleague 08:00 – 18:00 08:40 Family From Office Colleague 11:35 From Office From Office 17:55 15:20 Friend Colleague From Outside 21:30 Friend 7

Problem Formulation in a Single Network Input: G =( V,E L ,E U ,R L ,W ) V : Set of Users Friend Other E L ,R L : Labeled relationships ? ? ? E U : Unlabeled relationships Other Output: Input: f : G  R G =( V,E L ,E U ,R L ,W ) 8

Basic Idea Friend ? ? r 24 r 56 ? ? r 45 Relationship  Node Other 9

Partially Labeled Pairwise Factor Graph Model (PLP-FGM) Partially Labeled Constraint factor h y 21 =Friend y 21 = advisee Model h ( y 12 , y 21 ) y 21 PLP-FGM y 34 =? y 34 =? y 34 y 34 y 12 y 12 =Friend y 12 = advisor g ( y 45 , y 34 ) g ( y 12 , y 34 ) Latent Variable y 45 Input: Social Network g ( y 12 , y 45 ) y 16 =Other y 16 = coauthor f ( x 2 ,x 1 , y 21 ) v 3 f ( x 3 ,x 4 , y 34 ) v 4 f ( x 1 ,x 2 , y 12 ) Correlation factor g f ( x 3 ,x 4 , y 34 ) f ( x 4 ,x 5 , y 45 ) v 5 r 12 r 34 r 34 v 2 r 45 r 21 v 1 Problem: Attribute factors f relationships For each relationship, identify which type Input Model has the highest probability? Map relationship to nodes in model Example : Example : A makes call to B immediately after the call to C. Call frequency between two users? 10

Solutions ( con’t ) • Different ways to instantiate factors – We use exponential-linear functions • Attribute Factor: • Correlation / Constraint Factor: – Log-Likelihood of labeled Data: Parameters to estimate 11

Learning Algorithm • Maximize the log-likelihood of labeled relationships Expectation Computing Loopy Belief Propagation Gradient Ascent Method 12

Still Challenges? Questions: - How to obtain sufficiently training data? - Can we leverage knowledge from other network? 13

Inferring Social Ties Across Networks Output: Inferred social ties in Input: Heterogeneous Networks different networks Reviewer network Epinions Adam review Adam review distrust trust Product 1 Bob Bob distrust Chris trust Chris review review Danny Danny Product 2 Knowledge Transfer for Inferring Communication network Social Ties Mobile Both in office From Home Colleague 08:00 – 18:00 08:40 Family From Office Colleague 11:35 From Office From Office 17:55 15:20 Friend Colleague What is the knowledge to From Outside transfer? 21:30 Friend 14

Social Theories • Social balance theory • Structural hole theory • Social status theory • Two-step-flow theory Observations: (1) The underlying networks are unbalanced; (2) While the friendship networks are balanced. A A A A non-friend non-friend non-friend friend friend friend friend friend B C B C B C B C friend non-friend non-friend non-friend (A) (B) (C) (D) 15

Social Theories — Structural hole • Social balance theory • Structural hole theory • Social status theory • Two-step-flow theory Observations: Users are more likely (+25- 150% higher than change) to have the same type of relationship with C if C spans structural holes Structural hole 16

Social Theories — Social status • Social balance theory • Structural hole theory • Social status theory • Two-step-flow theory Observations: 99% of triads in the networks satisfy the social status theory Note: Given a triad (A,B,C), let us use 1 to denote the advisor-advisee relationship and 0 colleague relationship. Thus the number 011 to denote A and B are colleagues, B is C’s advisor and A is C’s advisor. 17

Social Theories — Two-step-flow • Social balance theory • Structural hole theory • Social status theory • Two-step-flow theory OL : Opinion leader; OU : Ordinary user. Observations: Opinion leaders are more likely (+71%-84% higher than chance) to have a higher social-status than ordinary users. 18

Transfer Factor Graph Model y 4 =? y 2 =? y 4 y 2 h ( y 3 , y 4 , y 5 ) TrFG model y 5 Coauthor y 1 y 5 =1 y 1 =1 y 3 Input: social network h ( y 1 , y 2 , y 3 ) y 6 network y 3 =0 y 6 =? f ( s 3 , s 3 , y 3 ) Triad-based factor 3 5 v 6 f ( u 5 , s 5 , y 5 ) v 4 f ( s 1 , u 2 , y 1 ) f ( u 2 , s 2 , y 2 ) | f ( u 4 , s 4 , y 4 ) v 3 4 6 u 2 , s 2 f ( s 6 , u 6 , y 6 ) 2 v 5 ( v 2 , v 3 ) u 4 , s 4 u 5 , s 5 v 2 u 1 , s 1 ( v 4 , v 5 ) u 3 , s 3 ( v 4 , v 6 ) u 6 , s 6 ( v 2 , v 1 ) 1 v 1 ( v 4 , v 3 ) ( v 6 , v 5 ) Observations Bridge via social theories y 4 =? y 2 =? y 4 y 2 h ( y 3 , y 4 , y 5 ) TrFG model y 5 y 1 y 5 =1 y 1 =1 y 3 Input: social network h ( y 1 , y 2 , y 3 ) y 6 y 3 =0 y 6 =? f ( s 3 , s 3 , y 3 ) 3 5 v 6 f ( u 5 , s 5 , y 5 ) mobile v 4 f ( s 1 , u 2 , y 1 ) f ( u 2 , s 2 , y 2 ) | f ( u 4 , s 4 , y 4 ) v 3 4 6 u 2 , s 2 f ( s 6 , u 6 , y 6 ) 2 v 5 ( v 2 , v 3 ) u 4 , s 4 u 5 , s 5 v 2 u 1 , s 1 ( v 4 , v 5 ) u 3 , s 3 ( v 4 , v 6 ) u 6 , s 6 ( v 2 , v 1 ) 1 v 1 ( v 4 , v 3 ) ( v 6 , v 5 ) Observations 19

Mathematical Formulation Features defined in Features defined in source network target network Triad-based features shared across networks 20

Data Sets • Epinions a network of product reviewers: 131,828 nodes (users) and 841,372 edges – trust relationships between users • Slashdot : 82,144 users and 59,202 edges – “friend” relationships between users • Mobile : 107 mobile users and 5,436 edges Undirected network – to infer friendships between users • Coauthor : 815,946 authors and 2,792,833 coauthor relationships – to infer advisor-advisee relationships between coauthors • Enron : 151 Enron employees and 3572 edges – to infer manager-subordinate relationships between users. Directed network 21

Results – undirected networks SVM and CRF are two baseline methods PFG is the proposed partially-labeled factor graph model TranFG is the proposed transfer – based factor graph model. 22

Results – directed networks SVM and CRF are two baseline methods PFG is the proposed partially-labeled factor graph model TranFG is the proposed transfer – based factor graph model. 23

Factor Contribution Analysis SH -Structural hole; OL -Opinion leader; SB -Social balance. SS -Social status. Undirected Network Directed Network 24

Conclusions and Future Work • Conclusions – different types of social ties have essentially different structural patterns in social networks; – By incorporating social theories, our proposed model can significantly improve (+4-14%) the inferring accuracy. • Future work – Inferring complex relationships between users, e.g., family, colleague, manager-subordinate; – Active learning for inferring social ties. 25

Thanks! HP: http://keg.cs.tsinghua.edu.cn/jietang/ System: http://arnetminer.org 26

Even complex than we imaged! • Only 16% of mobile phone users in Europe have created custom contact groups – users do not take the time to create it – users do not know how to circle their friends • The fact is that our social network is black - … 27

Example 2. Manager-employee relationship Enterprise email network CEO How to Manager infer Employee User interactions may form implicit groups 28

What is behind? Publication network Both in office From Home Twitter’s following network 08:00 – 18:00 08:40 From Office 11:35 From Office From 17:55 Office 15:20 From Outside 21:30 Mobile communication network 29