关键词: 非单调线搜索, 自适应BB步长, 非负矩阵分解

Abstract: Based on the Alternating Nonnegative Least Squares(ANLS) framework, an algorithm called Non-monotone Adaptive Barzilai-Borwein step-size (NABB) algorithm for nonnegative matrix factorization is proposed. The step-size of the algorithm satisfies the non-monotone line search though it is not obtained through line search, which ensures the global convergence of the algorithm. Furthermore, adaptive BB step-size and the gradient of the Lipschitz constant are also used to accelerate the rate of the convergence in this algorithm as usual. Finally, the algorithm is theoretically proved to be convergent. At the same time, the test results of numerical experiments and face recognition show that the proposed algorithm is effective and outruns other algorithms.

Key words: non-monotone line search, adaptive Barzilai-Borweinstep-size, nonnegative matrix factorization