A modified multiplicative update algorithm for euclidean distance-based nonnegative matrix factorization and its global convergence

Authors:
Ryota Hibi;Norikazu Takahashi
Affiliations:
Department of Informatics, Kyushu University, Nishi-ku, Fukuoka, Japan;Department of Informatics, Kyushu University, Nishi-ku, Fukuoka, Japan
Venue:
ICONIP'11 Proceedings of the 18th international conference on Neural Information Processing - Volume Part II
Year:
2011

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Abstract

Nonnegative matrix factorization (NMF) is to approximate a given large nonnegative matrix by the product of two small nonnegative matrices. Although the multiplicative update algorithm is widely used as an efficient computation method for NMF, it has a serious drawback that the update formulas are not well-defined because they are expressed in the form of a fraction. Furthermore, due to this drawback, the global convergence of the algorithm has not been guaranteed. In this paper, we consider NMF in which the approximation error is measured by the Euclidean distance between two matrices. We propose a modified multiplicative update algorithm in order to overcome the drawback of the original version and prove its global convergence.