Orthogonal nonnegative matrix tri-factorization for co-clustering: Multiplicative updates on Stiefel manifolds

Abstract

Matrix factorization-based methods become popular in dyadic data analysis, where a fundamental problem, for example, is to perform document clustering or co-clustering words and documents given a term-document matrix. Nonnegative matrix tri-factorization (NMTF) emerges as a promising tool for co-clustering, seeking a 3-factor decomposition X approximate to USVT with all factor matrices restricted to be nonnegative, i.e.. U >= 0.S >= 0, V >= 0. In this paper we develop multiplicative updates for orthogonal NMTF where X approximate to USVT is pursued with orthogonality constraints, (UU)-U-T = I. and (VV)-V-T = I, exploiting true gradients on Stiefel manifolds. Experiments on various document data sets demonstrate that our method works well for document clustering and is useful in revealing polysemous words via co-clustering words and documents. (C) 2010 Elsevier Ltd. All rights reserved.