Joint Elastic Net Regression and Nuclear Norm Subspace Clustering Algorithm

In subspace clustering, the data comprises points drawn from a collection of low-dimensional subspaces that are inherently embedded in a high-dimensional space. Self-representation methods learn an affinity matrix by expressing each sample as a linear combination of others. However, Sparse Subspace Clustering (SSC) enforces strict \(\ell _1\) -norm sparsity that becomes fragile when features are highly correlated, While Low-Rank Representation (LRR) is effective for capturing global structure via nuclear norm minimization, it can neglect locally discriminative patterns. To address these limitations, we propose Elastic Net Low-Rank Subspace Clustering (ENLRSC), which integrates elastic net regularization with nuclear norm constraints in a unified framework. The elastic net component combines \(\ell _1\) and F norm penalties to achieve both feature selection and the grouping effect, enabling robust handling of correlated features. Simultaneously, the nuclear norm captures global low-rank properties of the representation matrix. We develop an Inexact Augmented Lagrange Multiplier (IALM) algorithm with closed-form solutions for each subproblem. Extensive experiments on five benchmark datasets demonstrate that ENLRSC achieves substantial improvements over baseline methods in clustering accuracy and robustness.