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The rapid growth of Internet and modern technologies has brought data involving objects of multiple types that are related to each other, called as multi-type relational data. Traditional clustering methods for single-type data rarely work well on them, which calls for more advanced clustering techniques to deal with multiple types of data simultaneously to utilize their interrelatedness. A major challenge in developing simultaneous clustering methods is how to effectively use all available information contained in a multi-type relational data set including inter-type and intra-type relationships. In this paper, we propose a Symmetric Nonnegative Matrix Tri-Factorization (S-NMTF) framework to cluster multi-type relational data at the same time. The proposed S-NMTF approach employs NMTF to simultaneously cluster different types of data using their inter-type relationships, and incorporate the intra-type information through manifold regularization. In order to deal with the symmetric usage of the factor matrix in S-NMTF, we present a new generic matrix inequality to derive the solution algorithm, which involves a fourth-order matrix polynomial, in a principled way. Promising experimental results have validated the proposed approach.

Simultaneous clustering of multi-type relational data via symmetric nonnegative matrix tri-factorization