Global and local similarity learning in multi-kernel space for nonnegative matrix factorization

Abstract

Most of existing nonnegative matrix factorization (NMF) methods do not fully exploit global and local similarity information from data. In this paper, we propose a novel local similarity learning approach in the convex NMF framework, which encourages inter-class separability that is desired for clustering. Thus, the new model is capable of enhancing intra-class similarity and inter-class separability with simultaneous global and local learning. Moreover, the model learns the factor matrices in an augmented kernel space, which is a convex combination of pre-defined kernels with auto-learned weights. Thus, the learnings of cluster structure, representation factor matrix, and the optimal kernel mutually enhance each other in a seamlessly integrated model, which leads to informative representation. Multiplicative updating rules are developed with theoretical convergence guarantee. Extensive experimental results have confirmed the effectiveness of the proposed model.