the 2014 International Symposium on Nonlinear Theory and its Applications
A Generalized Sufficient Condition for Global Convergence of Modified Multiplicative Updates for NMF
Norikazu Takahashi, Jiro Katayama, Jun’ichi Takeuchi,
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Multiplicative updates are widely used computational methods for nonnegative matrix factorization (NMF). However, the global convergence of the original updates is not theoretically guaranteed. By the global convergence, we mean that the sequence of solutions contains at least one convergent subsequence and the limit of any convergent subsequence is a stationary point of the NMF optimization problem. In this paper, we consider a modified multiplicative update for a general error function and give a sufficient condition for the global convergence.