A NEW ACTIVE SET METHOD FOR NONNEGATIVE MATRIX FACTORIZATION

作者：Zhang Chao^*; Jing Liping; Xiu Naihua

来源：SIAM Journal on Scientific Computing, 2014, 36(6): A2633-A2653.

DOI：10.1137/130930212

• nonnegative matrix factorization
• proximal alternating nonnegative least squares
• active set method
• document clustering
• image classification

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.

• 出版日期2014
• 单位北京交通大学