Projected Gradient Methods for Nonnegative Matrix Factorization

2007/08/23 by Chih‐Jen Lin · 12 citations
Computer Science · Engineering · #Matrix Theory and Algorithms #Sparse and Compressive Sensing Techniques #Blind Source Separation Techniques

paper · doi:10.1162/neco.2007.19.10.2756

openalex publication_date 2007/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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.

Citations

• On search directions for minimization algorithms

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