Department of Computer Science, City University of Hong Kong, Tat Chee Avenue, Hong Kong; Shenzhen Research Institute, City University of Hong Kong, Shenzhen, China.
Neural Netw. 2018 Jul;103:63-71. doi: 10.1016/j.neunet.2018.03.003. Epub 2018 Mar 20.
This paper presents an algorithm for nonnegative matrix factorization based on a biconvex optimization formulation. First, a discrete-time projection neural network is introduced. An upper bound of its step size is derived to guarantee the stability of the neural network. Then, an algorithm is proposed based on the discrete-time projection neural network and a backtracking step-size adaptation. The proposed algorithm is proven to be able to reduce the objective function value iteratively until attaining a partial optimum of the formulated biconvex optimization problem. Experimental results based on various data sets are presented to substantiate the efficacy of the algorithm.
本文提出了一种基于双凸优化公式的非负矩阵分解算法。首先，引入了一个离散时间投影神经网络。推导了它的步长上限，以保证神经网络的稳定性。然后，基于离散时间投影神经网络和回溯步长自适应提出了一种算法。所提出的算法被证明能够迭代地减少目标函数值，直到达到所提出的双凸优化问题的局部最优解。基于各种数据集的实验结果证明了该算法的有效性。
