A novel study of kernel graph regularized semi-non-negative matrix factorization with orthogonal subspace for clustering

Abstract

As a nonlinear extension of Non-negative Matrix Factorization (NMF), Kernel Non-negative Matrix Factorization (KNMF) has demonstrated greater effectiveness in revealing latent features from raw data. Building on this, this paper introduces kernel theory and effectively combines the advantages of semi-nonnegative constraints, graph regularization, and orthogonal subspace constraints to propose a novel model-Kernel Graph Regularized Semi-Negative Matrix Factorization with Orthogonal Subspaces and Auxiliary Variables (semi-KGNMFOSV). This model introduces auxiliary variables and reformulates the optimization problem, successfully overcoming the convergence proof challenges typically associated with orthogonal subspace-constrained methods. Furthermore, the model utilizes kernel methods to effectively capture complex nonlinear structures in the data. The semi-nonnegative constraint, along with orthogonal subspace constraints incorporating auxiliary variables, enhances optimization efficiency, while graph regularization preserves the local geometric structure of the data. We develop an efficient optimization algorithm to solve the proposed model and conduct extensive experiments on multiple real-world datasets. Additionally, we investigate the impact of three different initialization strategies on the performance of the proposed algorithm. Experimental results demonstrate that, compared to classical and state-of-the-art methods, the proposed model exhibits superior performance across all three initialization strategies.