Negative Link Prediction in Social Media WSDM2015 1

Negative Link Prediction in Social Media

Jiliang Tang*, Shiyu Chang #, Charu Aggarwalⱡ and Huan Liu* *Data Mining and Machine Learning Lab, Arizona State University

#Beckman Institute, University of Illinois at Urbana-Champaign ⱡ IBM T.J. Watson Research Center

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Motivation

Negative Link Prediction

Unavailability Negative links are unwanted properties in online worlds Most social media sites allow positive links

― Friendships in Facebook ― Following in Twitter

Few social media sites allow negative links

Importance Negative links could be as important as positive links

Negative links have added value over positive links Negative links can help various online applications

—Positive link prediction —Recommendation

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Prevalently Available Sources in Social Media

Users:

Positive links:

Posting:

Interacting:

Content:

a b c d e

a 0 1 1 0 0

b 0 0 1 1 0

c 0 0 0 0 1

d 0 0 0 0 1

e 0 0 0 1 0

1 2 3 4

a 1 0 0 0

b 1 0 0 0

c 0 0 1 0

d 0 0 0 0

e 0 0 0 1

1 2 3 4

a 0 0 0 0

b 1 1 0 0

c 1 1 0 1

d 0 0 0 -1

e 0 0 -1 0

Positive Links Ap Authorship Matrix A Opinion Matrix O

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Problem Statement

a b c d e

a 0 1 1 0 0

b 0 0 1 1 0

c 0 0 0 0 1

d 0 0 0 0 1

e 0 0 0 1 0

1 2 3 4

a 1 0 0 0

b 1 0 0 0

c 0 0 1 0

d 0 0 0 0

e 0 0 0 1

1 2 3 4

a 0 0 0 0

b 1 1 0 0

c 1 1 0 1

d 0 0 0 -1

e 0 0 -1 0

Positive Links Ap Authorship Matrix A Opinion Matrix O

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Datasets

Epinions

– Trust and distrust links

Slashdot

– Friend and foe links

Reviews

Blogs

Writing Rating

Posting Replying/Commenting

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Where are our ``Foes’’?

We examine the typical structural relationships of “foes” within the positive network

– More than 45% within 2 hops

– More than 80% within 3 hops

1 2

3

5 4

6

2

Inf

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Social Theories

Balance Theory

– 92.31% and 93.01% triads in Epinions and Slashdot are balanced, respectively

Status Theory

– 94.73% and 93.38% of triads in Epinions and Slashdot satisfy status theory, respectively

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Negative Links and Negative Interactions

Negative links are positively correlated to negative

interactions

The more negative interactions two users have, the more likely a negative link exists between them

The random ratio is 2.4177e-04 and 3.9402e-04 in Epinions and Slashdot, respectively

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Our Findings

Most of our “foes” are close to us within a few (e.g.,2 or 3) hops in the positive network

Most of triads in signed networks satisfy balance theory and status theory

Pairs of users with negative interactions are more likely to have negative links than those without

Negative interactions between users increase the propensity of negative links

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A Classification Solution

Positive Negative and Missing

We consider the negative link prediction problem as a classification problem

– Missing links as positive samples PS

– Negative links as negative samples NS

Since missing and negative links are mixed together, it is challenging to construct labels

– Randomly select pairs as PS

– How to construct NS?

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Negative Sample Construction

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Considerations about the Basic Classifier

The classifier should be noise-tolerant

– Positive and negative samples contain noisy labels

We are able to capture reliability weights of samples

– Samples have different degrees of reliability

We are able to model balance theory

– Maintaining or increasing the structural balance with predicted negative links

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Capturing Reliability

The noise-tolerant SVM for the negative link prediction problem

Capturing reliability

– Positive samples > negative samples

– More negative interactions > less negative interactions

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Modeling Balance Theory

(u,v) have a positive link and w does not have positive links with both u and v

– If we want to maintain the structural balance, we can predict (u,w) and (v,w) as missing links

– If we want to increase the structural balance, we can predict (u,w) and (v,w) as negative links

u

v

w

u

v

w

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The Proposed Framework NeLP

NeLP is to solve the following optimization problem

Reliability of training

samples

Balance theory

Correlation and status theory

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Experimental Questions

Can negative links be predicted by the proposed framework NeLP?

How do various model components of NeLP contribute to the performance?

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Quality of Predicted Negative Links

Status theory can improve the performance of negative link prediction

The proposed framework NeLP can accurately predict negative links

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Component Analysis

We can perform component analysis by controlling their corresponding parameters

– Cn: negative samples

– cj: the j-th negative samples

– Cb: balance theory

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Future Work

The availability of negative links allow various social media applications

– Positive link prediction

– Recommendation

– Classification and clustering

We will investigate frameworks with other pervasively available sources

– User-generated content

– Cross media data

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Acknowledgements

Members of Data Mining and Machine Learning Lab at ASU

Funding Agencies: Army Research Office , The Office of Naval

Research and the Army Research Laboratory