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

摘要： 基于交替非负最小二乘算法的框架，提出一种非负矩阵分解的非单调自适应BB（Barzilai-Borwein）步长算法。虽然该算法的步长不是由线搜索取得的，但是满足非单调线搜索，从而保证了算法的全局收敛性。同时该算法使用自适应BB步长和梯度的Lipschitz常数来提高算法的收敛速度。最后在理论上证明了该算法是收敛的，同时数值试验和人脸识别的试验结果表明该算法是有效的且优于其他算法。

关键词: 非单调线搜索, 自适应BB步长, 非负矩阵分解