Nonconvex tensorial submodule clustering of 2-D images by mining local and global structural information

Abstract

Traditional subspace clustering methods convert each sample into a vector, which destroys the original spatial structure of the data and affects the clustering results. Therefore, we propose a novel submodule clustering method, NTSCLG, which twists each sample matrix and stacks them into a tensor, greatly preserving the intrinsic structure of the data. NTSCLG utilizes the t-product operator to generalize the traditional subspace representation to the free submodule union framework. The global structural characteristics of tensors are extracted using a nonconvex ${\ell }_q$-norm constraint, a symmetric uncertainty measure based on pointwise fuzzy mutual information (MI), a sparse ${\ell }_{2,log}$-norm constraint, and tensor low-rank constraint induced by log function. Notably, NTSCLG leverages tensor-based graph Laplacian local manifold regularization and the global dissimilarity matrix constructed from MI to enhance intra-cluster similarity and inter-cluster discrimination. Comprehensive experiments on multiple public datasets verify the effectiveness of the established NTSCLG algorithm, highlighting its superior clustering capability compared to existing methods.