Non-negative matrix factorization with L₀ sparseness constraints and its applications to face recognition

Article type: Research Article

Authors: Han, Dong | Gai, Shan^{; *}

Affiliations: School of Information Enginering, Nanchang Hangkong University, Nanchang, China

Correspondence: [*] Corresponding author. Shan Gai, School of Information Enginering, Nanchang Hangkong University, Nanchang, 330063, China. E-mail: gaishan@nchu.edu.cn.

Abstract: In order to solve the problem of unstable sparseness of non-negative matrix factorization (NMF), the improved NMF algorithms with L0 sparseness constraints are proposed. With the constraining the L0 norm of the coefficient matrix, we applied inverse matching principle into non-negative least square (ISNNLS) which enhances the reconstruction ability of the decomposition matrix. In addition, the L0 sparseness constraints are added to the basis matrix. In the updating process, the proposed algorithm set the smallest value to zero by projecting the basis vectors onto the closest non-negative vector with the expected sparseness. The experimental results have illustrated that the proposed algorithm can achieve higher reconstruction quality and effectiveness compared with the other algorithms.

Keywords: Sparseness, NMF, L₀ norm, sparse coding, feature extraction

DOI: 10.3233/JIFS-171116

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 1, pp. 729-737, 2018