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A NEW ACTIVE SET METHOD FOR NONNEGATIVE MATRIX FACTORIZATION
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DOI：10.1137/130930212.png)
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Nonnegative matrix factorization (NMF) is powerful in data analysis by recovering hidden features from redundant data. Recently, various extensions of NMF have been proposed to further enhance the classification results. In this paper, we present a novel proximal alternating nonnegative least squares (PANLS) framework for NMF. We show the globally convergent property that any accumulation point of PANLS is a stationary point of NMF. A new active set method based on the framework is proposed to solve each subproblem, which reduces to unconstrained optimization after finite steps and converges to the unique minimizer of the subproblem. The PANLS framework and the associated new active set method can be easily extended to variants of NMF. Extensive computational experiments using both synthetic data and real data show that our proposed method is attractive in terms of computational speed, the solution quality, and the flexibility to extensions of NMF.
Keyword:
nonnegative matrix factorization
proximal alternating nonnegative least squares
active set method
document clustering
image classification
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