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Predicting Positive and Negative Links in Online Social Networks

Predicting Positive and Negative Links in Online Social Networks. Jure Leskovec Stanford university, Daniel Huttenlocher , Jon Kleinberg Cornell University www 2010 2010-07-09 Presented by Seong yun Lee. Outline. Introduction Dataset Description Predicting Edge Sign

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Predicting Positive and Negative Links in Online Social Networks

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  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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