Predicting Positive and Negative Links in Online Social Networks

1. Predicting Positive and Negative Links in Online Social Networks Jure Leskovec Stanford university, Daniel Huttenlocher, Jon Kleinberg Cornell University www2010 2010-07-09 Presented by Seongyun Lee

2. Outline • Introduction • Dataset Description • Predicting Edge Sign • Connections to social-psychological theories • Global Structure of Signed Networks • The role of negative edges • Conclusion

3. Introduction • Social interaction on the Web involves both positive and negative relationships. • But, the vast majority of online social network research has considered only positive relationships 공감 비추는??

4. Introduction • The edge sign predicting problem • Attempt to infer the attitude of one user toward another • using the positive and negative relations that have been observed • Similar to the link prediction problem • Trust and distrust on Epinions by Guha et al. (13th WWW, 2004) • Evaluating propagation algorithms based on exponentiating the adjacency matrix • In this paper, • Using a machine-learning framework to solve this problem • Investigate generalization across Datasets. • Consider the link prediction problem

5. Dataset Description - Epinions (1/3) • Epinions • A product review Web site • (u,v) : whether u has expressed trust or distrust of user v (the review of v) • 119,217 nodes and 841,000 edges

6. Dataset Description - Slashdot (2/3) • Slashdot • A technology-related news website • (u,v) : u’s approval or disapproval of v’s comments • 82,144 users and 549,202 edges

7. Dataset Description - Wikipedia (3/3) • Wikipedia • A collectively authored encyclopedia with an active user community • (u,v) : whether u voted for or against the promotion of v to admin status • 103,747 votes and 7,118 users participating in the elections

8. Predicting Edge Sign (1/4) • A Machine-Learning Formulation • s(x,y) : sign of the edge (x,y) from x to y • s(x,y) = 1 : the sign of (x,y) is positive • s(x,y) = -1 : the sign of (x,y) is negative • s(x,y) = 0 : no directed edge from x to y • Features for predicting the sign of the edge from u to v • seven degree features • , , : the number of incoming positive and negative edges • : the number of outgoing positive and negative edges • : the total number of common neighbors of u and v (embeddedness) • : the total out-degree of u • : the total in-degree of v • 16 triad type features

9. Predicting Edge Sign (2/4) • triad type features • Based on social psychology • Understand the relationship between u and v through their joint relationships with third parties w • 16 possibilities • The edge between w and u : can be in either direction and of either sign • The edge between w and v : can be in either direction and of either sign w + - - + u v 2 * 2 * 2 * 2 = 16

10. Predicting Edge Sign (3/4) • Learning Methodology and Results • Using logistic regression classifier • x : vector of features (x1, … , xn) • b0, … , bn : coefficients based on the training data

11. Predicting Edge Sign (4/4) • Result • (A) Epinions (B) Slashdot (C) Wikipedia • Learned model prediction outperform propagation model • The edge signs can be meaningfully understood on local properties • At lowembeddedness, the triad features perform less than the degree features • But, the triad features become more effective as the embeddedness increases • The accuracy on the Wikipedia is lower than on the other networks • Unexpected Result • The Wikipedia is more publicly visible, consequential, information based than for the others • Interesting!

12. Connections to social-psychological theories • Balance Theory • “the friend of my friend is my friend.” • “the enemy of my friend is my enemy.” • “the friend of my enemy is my enemy.” • “the enemy of my enemy is my friend.”(less convincingly) • Status • A positive edge (x,y) : x regareds y as having higher status than herself • A negative edge (x,y) : x regareds y as having lower status than herself =

13. Connections to social-psychological theories • Comparison with the Learned Model : BFpm w U <=+ W =>- V + - - + u v

14. Connections to social-psychological theories • Bothsocial-psychological theories agree fairly well with the learned models • Balance theory’s disagree • When negative (u,w) and negative (w,v) edge suggest a positive (u,v) edge • “the enemy of my enemy is my friend.” • When positive(w,u) and positive(v,w)edge suggest a positive (u,v) edge • The direction from v to u rather than u to v • Need modifications of the models!

15. Connections to social-psychological theories • Comparison with Reduced Model • Balance theory : a theory of undirected graphs • Consider the learning model’s all edges as undirected • Apply logistic regression to four different triad types • Whether the undirected edge {u,w} is positive or negative • Whether the undirected edge {w,v} is positive or negative • Result (regression coefficients) • “enemy of my enemy” type (mm) : usually difficult condition

16. Connections to social-psychological theories • Comparison with Reduced Model • Status Theory • Reducing Model • Preprocessing the graph to flip the direction and sign of each negative edge. • Apply logistic regression to four different triad types • Whether the (u,w) edge is forward or backward • Whether the (w,v) edge is forward or backward • Result (regression coefficients) • The sign of the learned coefficient is the same as the sign of the status prediction

17. Generalization across datasets • How well the learned predictors generalize across the three datasets? • Experiments • For each pair of datasets, train the first dataset and evaluate it on the second data set • Result of 9 experiments using the All23 model • The off-digonal entries are nearly as high as the digonals • Very good generalization!!

18. Global Structure of Signed Networks • The theories of balance and status make global predictions about the pattern in the whole network • The global prediction of balance theory • The global prediction of status theory Let G be a signed, undirectedcomplete graph in which each triangle has an odd number of positive edges. Then the nodes of G can be partitioned into two sets A and B (where one of A or B may be empty), such that all edges within A and B are positive, and all edges with one end in A and the other in B are negative. Let G be a signed, directed tournament, and suppose that all sets of three nodes in G are status-consistent. Then it possible to order the nodes of G as v1, v2, . . . , vn in such a way that each positive edge (vi, vj) satisfies i < j, and each negative edge (vi, vj ) satisfies i > j.

19. Global Structure of Signed Networks • Experiment • Baseline dataset • Permuted-signs baseline : keep the structure and shuffle all the edge signs. • Rewired-edges baseline : keep the number of edges and the edge sings, shuffle the structure • Fraction of edges satisfying global balance and status • An evidence for a global status ordering exist, but very little evidence for the global presence of structural balance

20. The role of negative edges • How useful is it to know who a person’s enemies are, if we want to predict the presence of additional friends? • The experiments on two cases • Using the positive edges information • Using both the positive and negative edges information • Result

21. Conclusion • This paper’s method yield significantly improved performance • There is evidence in our dataset for global status ordering • Very good generalization • Negative relationship can be useful problem of link prediction for positive edges • Further work • Expansion to not explicitly tagged domains

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