# Hierarchical Probabilistic Matrix Factorization with Network Topology for Multi-relational Social Network

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Haoli Bai,
Zenglin Xu,
Bin Liu,
Yingming Li
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Proceedings of The 8th Asian Conference on Machine Learning, PMLR 63:270-285, 2016.

#### Abstract

Link prediction in multi-relational social networks has attracted much attention. For instance, we may care the chance of two users being friends based on their contacts of other patterns, e.g., SMS and phone calls. In previous work, matrix factorization models are typically applied in single-relational networks; however, two challenges arise to extend it into multi-relational networks. First, the interaction of different relation types is hard to be captured. The second is the cold start problem, as the prediction of new entities in multi-relational networks becomes even more challenging. In this article we propose a novel method called Hierarchical Probabilistic Matrix Factorization with Network Topology (HPMFNT). Our model exploits the network topology by extending the Katz index into multi-relational settings, which could efficiently model the multidimensional interplay via the auxiliary information from other relationships. We also utilize the extended Katz index along with entitiy attributes to solve the cold-start problem. Experiments on two real world datasets have shown that our model outperforms the state-of-the-art with a significant margin.

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