Single multiplicatively updated matrix factorization for co-clustering

Abstract

Co-clustering treats a data matrix in a symmetric fashion that a partitioning of rows can induce a partitioning of columns, and vice versa. It has been shown to be advantageous over traditional clustering. However, the time and space complexities of most co-clustering algorithms are costly which limit their effectiveness on large datasets. To address this problem, we propose a single multiplicatively updated matrix factorization for co-clustering, in which only one factor matrix needs to be updated by a multiplicative rule derived from nonnegative matrix tri-factorization (NMTF) and other matrices can be obtained from alternative nonnegative least squares. Moreover, we extend this hybrid method to symmetric NMTF that is conducted on proximity matrix. Extensive experiments on several large text datasets show that our approach outperforms state-of-the-art co-clustering algorithms in terms of purity and entropy but with much less time and space costs.