Manifold regularized non-negative matrix factorization with label information

Abstract

Non-negative matrix factorization (NMF) as a popular technique for finding parts-based, linear representations of non-negative data has been successfully applied in a wide range of applications, such as feature learning, dictionary learning, and dimensionality reduction. However, both the local manifold regularization of data and the discriminative information of the available label have not been taken into account together in NMF. We propose a new semisupervised matrix decomposition method, called manifold regularized non-negative matrix factorization (MRNMF) with label information, which incorporates the manifold regularization and the label information into the NMF to improve the performance of NMF in clustering tasks. We encode the local geometrical structure of the data space by constructing a nearest neighbor graph and enhance the discriminative ability of different classes by effectively using the label information. Experimental comparisons with the state-of-the-art methods on theCOIL20, PIE, Extended Yale B, and MNIST databases demonstrate the effectiveness of MRNMF.