Adaptive graph regularized Nonnegative Matrix Factorization via feature selection

Nonnegative Matrix Factorization (NMF), a popular compact data representation method, fails to discover the intrinsic geometrical structure of the data space. Graph regularized NMF (GrNMF) is proposed to avoid this limitation by regularizing NMF with a nearest neighbor graph constructed from the input data feature space. However using the original feature space directly is not appropriate because of the noisy and irrelevant features. In this paper, we propose a novel data representation algorithm by integrating feature selection and graph regularization for NMF. Instead of using a fixed graph as GrNMF, we regularize NMF with an adaptive graph constructed according to the feature selection results. A uniform object is built to consider feature selection, NMF and adaptive graph regularization jointly, and a novel algorithm is developed to update the graph, feature weights and factorization parameters iteratively. Data clustering experiment shows the efficacy of the proposed method on the Yale database.