Predicting positive and negative links in online social networks
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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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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


Outline

  • Introduction

  • Dataset Description

  • Predicting Edge Sign

  • Connections to social-psychological theories

  • Global Structure of Signed Networks

  • The role of negative edges

  • Conclusion


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??


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


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


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


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


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


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


    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


    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!


    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

        =


    Connections to social-psychological theories

    • Comparison with the Learned Model

      :

    BFpm

    w

    U <=+ W =>- V

    +

    -

    -

    +

    u

    v


    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!


    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


    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


    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!!


    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.


    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


    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


    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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