Using the genetic algorithm to enhance nonnegative matrix factorization initialization

Nonnegative matrix factorization (NMF) algorithms have been utilized in a wide range of real applications; however, the performance of NMF is highly dependent on three factors including: (1) choosing a problem dependent cost function; (2) using an effective initialization method to start the updating procedure from a near-optimal point; and (3) determining the rank of factorized matrices prior to decomposition. Due to the nonconvex nature of the NMF cost function, finding an analytical-based optimal solution is impossible. This paper is aimed at proposing an efficient initialization method to modify the NMF performance. To widely explore the search space for initializing the factorized matrices in NMF, the island genetic algorithm (IGA) is employed as a diverse multiagent search scheme. To adapt IGA for NMF initialization, we present a specific mutation operator. To assess how the proposed IGA initialization method efficiently enhances NMF performance, we have implemented state-of-the-art initialization methods and applied to the Japanese Female Facial Expression dataset to recognize the facial expression states. Experimental results demonstrate the superiority of the proposed approach to the compared methods in terms of relative error and fast convergence.