An alternating nonmonotone projected Barzilai–Borwein algorithm of nonnegative factorization of big matrices

摘要

In this paper, a new alternating nonmonotone projected Barzilai–Borwein (BB) algorithm is developed for solving large scale problems of nonnegative matrix factorization. Unlike the existing algorithms available in the literature, a nonmonotone line search strategy is proposed to find suitable step lengths, and an adaptive BB spectral parameter is employed to generate search directions such that the constructed subproblems are efficiently solved. Apart from establishment of global convergence for this algorithm, numerical tests on three synthetic datasets, four public face image datasets and a real-world transcriptomic dataset are conducted to show advantages of the developed algorithm in this paper. It is concluded that in terms of numerical efficiency, noise robustness and quality of matrix factorization, our algorithm is promising and applicable to face image reconstruction, and deep mining of transcriptomic profiles of the sub-genomes in hybrid fish lineage, compared with the state-of-the-art algorithms.