Orthogonal Nonnegative Matrix Factorization for Multi-type Relational Clustering

Relational clustering with heterogeneous data objects has impact in various important applications, such as web mining, text mining and bioinformatics etc. In this paper, we build a star-structured general model for relational clustering. It is formulated as an orthogonal tri-nonnegative matrix factorization. The model performs matrix approximation among all different data types to look for hidden cluster structure. Under this model, we propose a multiplicative update algorithm to minimize the matrix approximation error for simultaneously clustering of heterogeneous relational objects. The proposed algorithm tries to retain the orthogonality of indicator matrices, which make it easier for result interpretation. We also prove the correctness and convergence of the algorithm under the proposed iterative update rules. Experiments demonstrate the effectiveness of the proposed algorithm and the ability to co-cluster different data objects. Keywords-relational clustering; co-clustering; nonnegative matrix factorization; clustering