## Prediction and Clustering in Signed Networks: A Local to Global Perspective

Kai-Yang Chiang, Cho-Jui Hsieh, Nagarajan Natarajan, Inderjit S. Dhillon, Ambuj Tewari; 15(34):1177−1213, 2014.

### Abstract

The study of social networks is a burgeoning research area. However, most existing work is on networks that simply encode whether relationships exist or not. In contrast, relationships in signed networks can be positive (âlike", âtrust") or negative (âdislike", âdistrust"). The theory of social balance shows that signed networks tend to conform to some local patterns that, in turn, induce certain global characteristics. In this paper, we exploit both local as well as global aspects of social balance theory for two fundamental problems in the analysis of signed networks: sign prediction and clustering. Local patterns of social balance have been used in the past for sign prediction. We define more general measures of social imbalance (MOIs) based on $\ell$-cycles in the network and give a simple sign prediction rule. Interestingly, by examining measures of social imbalance, we show that the classic Katz measure, which is used widely in unsigned link prediction, also has a balance theoretic interpretation when applied to signed networks. Motivated by the global structure of balanced networks, we propose an effective low rank modeling approach for both sign prediction and clustering. We provide theoretical performance guarantees for our low-rank matrix completion approach via convex relaxations, scale it up to large problem sizes using a matrix factorization based algorithm, and provide extensive experimental validation including comparisons with local approaches. Our experimental results indicate that, by adopting a more global viewpoint of social balance, we get significant performance and computational gains in prediction and clustering tasks on signed networks. Our work therefore highlights the usefulness of the global aspect of balance theory for the analysis of signed networks.

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