Robust Nonnegative Matrix Factorization with Discriminability for image representation

Due to its psychological and physiological interpretation of naturally occurring data, Nonnegative Matrix Factorization (NMF) has attracted considerable attention for learning effective representation for images. And its graph-regularized extensions have shown promising results by exploiting the low dimensional manifold structure of data. Actually, their performance can be further improved because they still suffer from several important problems, i.e., sensitivity to noise in data, trivial solution problem, and ignoring the discriminative information. In this paper, we propose a novel method, referred to as Robust Nonnegative Matrix Factorization with Discriminability (RNMFD), for image representation, which can effectively and simultaneously cope with problems mentioned above by imposing a sparse noise matrix for data reconstruction and approximate orthogonal constraints. We carried out extensive experiments on five benchmark image datasets and the results demonstrate the superiority of our RNMFD in comparison with several state-of-the-art methods.