Constrained non-negative matrix factorization with graph Laplacian

Abstract

Non-negative Matrix Factorization (NMF) is proven to be a very effective decomposition method for dimensionality reduction in data analysis, and has been widely applied in computer vision, pattern recognition and information retrieval. However, NMF is virtually an unsupervised method since it is unable to utilize prior knowledge about data. In this paper, we present Constrained Non-negative Matrix Factorization with Graph Laplacian (CNMF-GL), which not only employs the geometrical information, but also properly uses the label information to enhance NMF. Specifically, we expect that a graph regularized term could preserve the local structure of original data, meanwhile data points both having the same label and possessing different labels will have corresponding constraint conditions. As a result, the learned representations will have more discriminating power. The experimental results on image clustering manifest the effectiveness of our algorithm.