Sparse concept discriminant matrix factorization for image representation

Over the past few decades, matrix factorization has attracted considerable attention for image representation. It is desired for a matrix factorization technique to find the basis that is able to capture highly discriminant information as well as to preserve the intrinsic manifold structure. Besides, the basis has to generate a sparse representation for a given image. In this paper, we propose a matrix factorization method called Sparse concept Discriminant Matrix Factorization (SDMF) by combining a novel fisher-like criterion with the sparse coding. The criterion is discriminant enough across different feature spaces, and meanwhile maintains locally neighboring structures. The proposed method is general for both cases with and without class labels, hence yielding supervised and un-supervised SDMFs. Experimental results show that SDMF provides better representation with higher performance on two tasks (image recognition and clustering) compared with the existing matrix factorization methods.