Joint sample-feature subspace learning via bidirectional reconstruction for feature selection

Subspace learning provides a powerful way to analyze high-dimensional data by identifying low-dimensional structures that capture its most informative patterns. Yet, many existing approaches overlook the dual roles played by both features and samples, leading to representations that miss important joint dependencies essential for effective feature selection and representation learning. To address this limitation, we propose a unified framework termed Joint Sample-Feature Subspace Learning via Bidirectional Reconstruction for Feature Selection (JSF-BRFS). The proposed model formulates a joint optimization problem that simultaneously learns sample-level and feature-level representations under a bidirectional reconstruction scheme. JSF-BRFS integrates two complementary self-representation processes—one in the feature domain and the other in the sample domain—while enforcing mutual consistency between their latent subspaces through symmetric cross-space coupling. To enhance representation quality, we further incorporate structural constraints that promote independence, interpretability, and locality preservation in the learned bases. To efficiently solve the resulting nonconvex optimization problem, we develop a Sequential Nonsmooth Programming algorithm that finds a Karush-Kuhn-Tucker point for the corresponding penalized problem. Comprehensive experiments conducted on multiple benchmark datasets show that JSF-BRFS consistently surpasses state-of-the-art feature selection methods in both clustering accuracy and feature selection performance.