Robust sparse nonnegative matrix factorization based on maximum correntropy criterion

Abstract

Nonnegative matrix factorization (NMF) is a significant matrix decomposition technique for learning parts-based, linear representation of nonnegative data, which has been widely used in a broad range of practical applications such as document clustering, image clustering, face recognition and blind spectral unmixing. Traditional NMF methods, which mainly minimize the square of the Euclidean distance or the Kullback-Leibler (KL) divergence, seriously suffer the outliers and non-Gaussian noises. In this paper, we propose a robust sparse nonnegative matrix factorization algorithm, called l1-norm nonnegative matrix factorization based on maximum correntropy criterion (11-CNMF). Specifically, l1-CNMF is derived from the traditional NMF algorithm by incorporating the l1 sparsity constraint and maximum correntropy criterion. Numerical experiments on the Yale database and the ORL database with and without apparent outliers show the effectiveness of the proposed algorithm for image clustering compared with other existing related methods.