A nonnegative matrix factorization algorithm based on a discrete-time projection neural network

• Published in: Neural networks Vol. 103; pp. 63 - 71
• Main Authors: Che, Hangjun, Wang, Jun
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 01.07.2018
• Subjects: Algorithms; Biconvex optimization; Databases, Factual - utilization; Discrete-time projection neural network; Neural Networks (Computer); Nonnegative matrix factorization; Pattern Recognition, Automated - methods; Pattern Recognition, Automated - trends; Photic Stimulation - methods; Time Factors; Biconvex optimization; Nonnegative matrix factorization; Discrete-time projection neural network
• ISSN: 0893-6080; 1879-2782; 1879-2782
• DOI: 10.1016/j.neunet.2018.03.003

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.