Orthogonal Nonnegative Matrix Factorization: Multiplicative Updates on Stiefel Manifolds

Abstract

Nonnegative matrix factorization (NMF) is a popular method for multivariate analysis of nonnegative data, the goal of which is decompose a data matrix into a product of two factor matrices with all entries in factor matrices restricted to be nonnegative. NMF was shown to be useful in a task of clustering (especially document clustering). In this paper we present an algorithm for orthogonal nonnegative matrix factorization, where an orthogonality constraint is imposed on the nonnegative decomposition of a term-document matrix. We develop multiplicative updates directly from true gradient on Stiefel manifold, whereas existing algorithms consider additive orthogonality constraints. Experiments on several different document data sets show our orthogonal NMF algorithms perform better in a task of clustering, compared to the standard NMF and an existing orthogonal NMF.KeywordsNonnegative Matrix FactorizationDocument ClusterOrthogonality ConstraintMultiplicative UpdateProbabilistic Latent Semantic IndexingThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.