Semi-supervised least squares nonnegative matrix factorization and graph-based extension

Nonnegative matrix factorization (NMF) has been widely used in information retrieval, computer vision, and face recognition because it captures the underlying intrinsic structure of data by using its parts-based representations in the low dimensional space. In this paper, we first propose a novel semi-supervised least squares NMF (SLSNMF) method. This SLSNMF uses hyperplanes to separate the labelled points from different classes and minimizes the least squares loss. By considering the maximum margin principle, the discriminative abilities of clustering representations are greatly enhanced. We further present a graph-based least squares NMF (GLSNMF) method by incorporating the local manifold regularization into SLSNMF. Clustering experiments on five popular databases verify the effectiveness of our proposed SLSNMF and GLSNMF compared to the other state-of-the-art methods.