Non-Negative Matrix Factorization With Locality Constrained Adaptive Graph

Non-negative matrix factorization (NMF) has recently attracted much attention due to its good interpretation in perception science and widely applications in various fields. In this paper, a novel graph regularized NMF algorithm called NMF with locality constrained adaptive graph (NMF-LCAG) is proposed. Compared with other NMF based algorithms, the proposed NMF-LCAG algorithm has the following advantages: 1) Unlike the traditional NMF method which neglects the geometric information of original data, the proposed algorithm introduces a locality constrained graph to discover the latent manifold structure of the data and 2) Different from most graph regularized NMF algorithms in which the graphs are predefined and kept unchanged during the NMF procedure, two locality constraint terms are employed in our NMF-LCAG to adaptively optimize the graph. Thus, the weight matrix of graph and low dimensional features of data can be simultaneously learned by our algorithm, which makes NMF-LCAG more flexible than other approaches. Moreover, an iterative updating strategy is developed to optimize the objective function of our algorithm and the convergence analysis is also given. Extensive experiments are conducted on four face image databases and three UCI datasets to demonstrate the effectiveness of the proposed NMF-LCAG algorithm. Compared with some other related algorithms, the proposed NMF-LCAG algorithm can achieve at least 1% ~ 3% accuracy improvement in most cases.