Dual Graph Regularized Sparse Nonnegative Matrix Factorization for Data Representation

Nonnegative matrix factorization (NMF) has been a state-of-the-art data representation method, since it contains the psychological and physiological evidence for parts-based representation in the human brain. However, many existing NMF methods fail to ensure the decomposed results to be sparse, or ignore some useful geometrical structure information in the data. In this paper, a sparse NMF method, called dual graph regularized nonnegative matrix factorization with l(1)-norm sparsity constraint (l(1)-DNMF) is proposed to solve the two problems together. In addition, to satisfy the locality condition and sparsity constraint simultaneously, we also propose the dual graph regularized nonnegative matrix factorization with local coordinate constraint (LDNMF). By using the multiplicative update algorithm to solve the optimization problems of l(1)-DNMF and LDNMF, we derive two efficient alternating iterative methods. Experimental results on four image datasets demonstrate the promising performance of the new methods compared with several related methods for clustering applications.