Semi-supervised non-negative matrix tri-factorization with adaptive neighbors and block-diagonal learning

Abstract

Graph-regularized non-negative matrix factorization (GNMF) is proved to be effective for the clustering of nonlinear separable data. Existing GNMF variants commonly improve model performance by adding different additional constraints or refining the model factorization form, which can lead to problems such as increased algorithm complexity or insufficient performance release. In this paper, we propose semi-supervised non-negative matrix tri-factorization with adaptive neighbors and block-diagonal (ABNMTF). Different from existing methods, in ABNMTF the similarity graph matrix is learned from the original data by adaptive neighbors k-nearest model, and a block diagonal matrix is constructed based on a few labeled data to update the similarity matrix. Our approach reconstructs the block diagonal structure into the adaptive similarity matrix, which enables simultaneous learning of the similarity matrix and label binding during factorization, engendering a distinguishable subspace representation matrix and therefore improving the clustering performance without significantly increasing the complexity of the algorithm. We also represent an optimization method to solve the ABNMTF and provide analyses of convergence and computational complexity. Extensive experiments on 8 real image datasets show that the proposed algorithm reports superior performance against several state-of-the-art approaches. Code has been made available at:https://github.com/LstinWh/ABNMTF.