Efficient algorithms of box-constrained Nonnegative Matrix Factorization and its applications in image clustering

Abstract

Nonnegative Matrix Factorization (NMF) provides an important approach of unsupervising learning, but it faces computational challenges when applied into clustering of high-dimensional datasets. In this paper, a class of novel nonmonotone gradient-descent algorithms are developed for solving box-constrained NMF problems. Unlike existing algorithms in the literature that update each matrix factor individually by fixing another one, our algorithms simultaneously update the paired matrix factors by leveraging adaptive projected Barzilai-Borwein directions and appropriate step sizes generated by the developed nonmonotone line search rules. Theoretically, it is proved that the developed algorithms are well defined and globally convergent. Extensive numerical tests on public image datasets demonstrate that the developed algorithms in this paper outperform the state-of-the-art ones, in terms of clustering performance, computational efficiency, and robustness of mining noisy data.