Non-negative Matrix Factorization with Symmetric Manifold Regularization

Non-negative matrix factorization (NMF) is becoming an important tool for information retrieval and pattern recognition. However, in the applications of image decomposition, it is not enough to discover the intrinsic geometrical structure of the observation samples by only considering the similarity of different images. In this paper, symmetric manifold regularized objective functions are proposed to develop NMF based learning algorithms (called SMNMF), which explore both the global and local features of the manifold structures for image clustering and at the same time improve the convergence of the graph regularized NMF algorithms. For different initializations, simulations are utilized to confirm the theoretical results obtained in the convergence analysis of the new algorithms. Experimental results on COIL20, ORL, and JAFFE data sets demonstrate the clustering effectiveness of the proposed algorithms by comparing with the state-of-the-art algorithms.