JCSE, vol. 4, no. 2, pp.97-109, 2010

DOI:

Nonnegative Matrix Factorization with Orthogonality Constraints

Jiho Yoo, Seungjin Choi
Department of Computer Science and Engineering, Pohang University of Science and Technology, Korea

Abstract: Nonnegative matrix factorization (NMF) is a popular method for multivariate analysis ofnonnegative data, which is to decompose a data matrix into a product of two factor matriceswith all entries restricted to be nonnegative. NMF was shown to be useful in a task of clustering(especially document clustering), but in some cases NMF produces the results inappropriate tothe clustering problems. In this paper, we present an algorithm for orthogonal nonnegativematrix factorization, where an orthogonality constraint is imposed on the nonnegativedecomposition of a term-document matrix. The result of orthogonal NMF can be clearlyinterpreted for the clustering problems, and also the performance of clustering is usually betterthan that of the NMF. We develop multiplicative updates directly from true gradient on Stiefelmanifold, whereas existing algorithms consider additive orthogonality constraints. Experimentson several different document data sets show our orthogonal NMF algorithms perform better ina task of clustering, compared to the standard NMF and an existing orthogonal NMF.

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