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Projected gradient methods for nonnegative matrix factorization. (English) Zbl 1173.90583
Summary: Nonnegative matrix factorization (NMF) can be formulated as a minimization problem with bound constraints. Although bound-constrained optimization has been studied extensively in both theory and practice, so far no study has formally applied its techniques to NMF. In this letter, we propose two projected gradient methods for NMF, both of which exhibit strong optimization properties. We discuss efficient implementations and demonstrate that one of the proposed methods converges faster than the popular multiplicative update approach. A simple Matlab code is also provided.

MSC:
90C52 Methods of reduced gradient type
90C30 Nonlinear programming
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