What Is the Added Value of Negative Links in Online Social Networks?

Jérôme Kunegis, Julia Preusse, Felix SchwagereitInstitute for Web Science and Technologies (WeST), University of Koblenz–Landau

We thank Paolo Massa for providing the Epinions dataset. The research leading to these results has received funding from the European Community's Seventh Framework Programme under grant agreement n° 257859, ROBUST.

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Social Networks: Ties between People

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Some People Don't Like Each Other

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Real Social Networks Contain Negative Ties

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Online Social Networks Have Many Forms of Positive Links

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Where Are the Negative Ties?

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They Are on Slashdot.org

79,120 users; 392,326 positive ties; 123,255 negative ties

http://konect.uni-koblenz.de/test/networks/slashdot-zoo

[1] J. Kunegis, A. Lommatzsch, C. Bauckhage. The Slashdot Zoo: Mining a Social Network with Negative Edges. In Proc. WWW, pages 741– 750, 2009.

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And Epinions.com

131,828 users; 717,667 positive ties; 123,705 negative ties

http://konect.uni-koblenz.de/networks/epinions

[2] P. Massa, P. Avesani. Controversial users demand local trust metrics: an experimental study on epinions.com community. In Proc. AAAI, pages 121– 126, 2005.

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What Is the Added Value of Negative Links?

Pro: More information about the community

Con: More negativity in the community

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Pro: More information about the community

Really?

What Is the Added Value of Negative Links?

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Our Idea

If negative links can be predicted from positive ones, then

negative links do not bring any added

value to the network

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Machine Learning Task

Prediction

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Related Problem: Prediction of Future Ties (Link Prediction)

Prediction

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Indicators for Link Prediction

?Neighborhood-basedCentrality-based

➔Common neighbors➔Cosine similarity➔Jaccard coefficient➔Adamic–Adar➔Exponential/Neuman graph kernel➔Paths of length 3

➔Degree➔PageRank

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Centrality-based Indicators

DegreePageRank

u v

f(u, v) = d(u) d(v)f(u, v) = PR(u) PR(v)

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Neighborhood-based Indicators

Common neighborsJaccard indexCosine similarity

A B

u v

f(u, v) = |A Ո B|f(u, v) = |A Ո B| / |A U B|f(u, v) = |A Ո B| / sqrt(|A| |B|)

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Link Prediction: Edge vs No Edge

?tie

no tie

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Our Task: Positive Edge vs Negative Edge vs No Edge

?pos. tie

neg. tie

no tie

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A Good and Simple Idea Which Does Not Work

?

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Learning Feature Weights by Regression

Dataset Degree PageRank Common neighbors

Paths of length 3

Cosine similarity

Slashdot 0.2502 0.2321 −0.5411 −0.4866 −3.9434

Epinions −0.0105 0.8498 −0.8587 −0.3827 −5.0360

Centrality-based Neighborhood-based

Preferential attachmentholds for

negative edges

Conflictis avoided

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Measuring Prediction Accuracy

(1) Neg-tie vs Pos-tie + No-tie

(2) Neg-tie vs No-tie

(3) Neg-tie vs Pos-tie

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Prediction Accuracy

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Let's Look at the Data

Slashdot Epinions

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Combine PageRank and Cosine Similarity

f = ® ({ ) − ̄ log(cos)log(PR) if cos = 0min(log(PR)) otherwise

Slashdot Epinions

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Evaluation

All >0.5

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How Much Better Does It Get If We Have Negative Links?

The “enemy” function adds 0.05 points

of AUC to knowing negative ties

http://konect.uni-koblenz.de/

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@kunegis

Thank You!