Unified Framework for Faster Clustering via Joint Schatten p-Norm Factorization With Optimal Mean

To enhance the effectiveness and efficiency of subspace clustering in visual tasks, this work introduces a novel approach that automatically eliminates the optimal mean, which is embedded in the subspace clustering framework of low-rank representation (LRR) methods, along with the computationally factored formulation of Schatten <inline-formula> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula>-norm. By addressing the issues related to meaningful computations involved in some LRR methods and overcoming biased estimation of the low-rank solver, we propose faster nonconvex subspace clustering methods through joint Schatten <inline-formula> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula>-norm factorization with optimal mean (JS<inline-formula> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula>NFOM), forming a unified framework for enhancing performance while reducing time consumption. The proposed approach employs tractable and scalable factor techniques, which effectively address the disadvantages of higher computational complexity, particularly when dealing with large-scale coefficient matrices. The resulting nonconvex minimization problems are reformulated and further iteratively optimized by multivariate weighting algorithms, eliminating the need for singular value decomposition (SVD) computations in the developed iteration procedures. Moreover, each subproblem can be guaranteed to obtain the closed-form solver, respectively. The theoretical analyses of convergence properties and computational complexity further support the applicability of the proposed methods in real-world scenarios. Finally, comprehensive experimental results demonstrate the effectiveness and efficiency of the proposed nonconvex clustering approaches compared to existing state-of-the-art methods on several publicly available databases. The demonstrated improvements highlight the practical significance of our work in subspace clustering tasks for visual data analysis. The source code for the proposed algorithms is publicly accessible at <uri>https://github.com/ZhangHengMin/TRANSUFFC</uri>.