1. Predicting Positive and Negative Links in Online Social Networks
Jure Leskovec
Stanford university,
Daniel Huttenlocher, Jon Kleinberg
Cornell University
www 2010
Presented by Seong yun 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 In this paper,
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)
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)
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)
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
2 * 2 * 2 * 2 = 16 u w v + -

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 low embeddedness, 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 theoriesu w v + -
Comparison with the Learned Model :
BFpm
U <=+ W =>- V

14. Connections to social-psychological theories
Both social-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, undirected complete 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

22. 끝 끝