Graph regularized non-negative matrix factorization with sparse coding

Matrix factorization techniques have been frequently utilized in pattern recognition and machine learning. Among them, Non-negative Matrix Factorization (NMF) has received considerable attention because it represents the naturally occurring data by parts of it. On the other hand, from the geometric perspective, the data is usually sampled from a low dimensional manifold embedded in a high dimensional ambient space. One hopes then to find a compact representation which uncovers the intrinsic geometric structure. In this paper, we propose a novel method, called Graph Regularized Non-negative Matrix Factorization with Sparse Coding (GRNMF_SC), the new model can learn much sparser representation and more discriminating power via imposing sparse constraint and Laplacian regularization explicitly. Experimental results on the ORL and Yale databases demonstrate encouraging performance of the proposed algorithm when compared with the state-of-the-art algorithms.