Regularized Semi-Supervised Subspace Clustering with Local-Structure-Preservation-Based Soft-MFA

Semi-supervised subspace clustering (SSC) algorithms utilize partially labeled data to improve clustering performance. However, existing SSC methods often focus on the global similarity structure of data and neglect the local structure to some extent. To address this limitation, we propose a soft marginal Fisher analysis (SMFA) based regularization term to constrain the data after projection, preserving the intraclass similarity and enhancing interclass discrimination in the low-dimensional space. By incorporating the SMFA regularization term, the proposed SSC framework encourages low-rank subspaces to separate data points from different classes while grouping together data points from the same class. Furthermore, by employing high-resolution ordinary differential equations (ODEs), our study explores the convergence dynamics of the alternating direction method of multiplier (ADMM) in addressing low-rank representation (LRR) challenges. Experimental results on five publicly available databases demonstrate that our proposed method outperforms state-of-the-art SSC methods in terms of clustering accuracy and stability. These results demonstrate the effectiveness of our proposed regularization term and its ability to preserve both the global and local similarity structure of data in low-rank subspaces.