Global and Local Similarity Learning in Multi-Kernel Space for Nonnegative Matrix Factorization

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.