A unified one-step joint optimization framework for sparse subspace clustering and self-constrained spectral clustering

Subspace clustering aims to explore multiple low-dimensional subspaces within data to more effectively represent the essential structure of high-dimensional datasets. Traditional subspace clustering methods typically employ a two-step strategy: first, constructing a similarity matrix based on the relevance between samples, and then performing spectral clustering on this matrix. Although these approaches achieve local optimality at each stage, they do not guarantee the global optimality of the clustering results. To address these issues, this study introduces an algorithm that integrates subspace clustering and spectral clustering, enabling the simultaneous optimization of the similarity matrix and the clustering indicator matrix in a low-dimensional space. In the subspace clustering module, an -ℓ0,2norm constraint is applied to the self-representation coefficient matrix to enhance the sparsity of the similarity matrix. For the spectral clustering component, we employ self-constrained spectral clustering to improve the graph-cut performance, resulting in higher-quality clustering indicator matrices. To integrate the two components, we develop a unified one-step joint optimization framework that addresses the clustering problem through a proximal alternating minimization approach with proven convergence. Its innovation lies in constructing a simultaneous optimization model for the similarity and cluster indicator matrices, effectively solved using the proximal alternating minimization (PAM) method to tackle the problem's inherent nonlinearity. The proposed algorithm has demonstrated strong performance across various datasets, outperforming eight representative comparison algorithms.