Learnable Unified Structure under Global-Local Consistency for Unsupervised Feature Selection

Abstract Previous unsupervised feature selection methods typically model global data distributions and local geometric structures separately or via parallel constraints. Such decoupled modeling often leads to structural inconsistencies due to the lack of a unified representation of sample relationships. Moreover, existing local structure-based methods generally rely on predefined and fixed adjacency graphs, which often contain noise and redundancy, further degrading the learning performance. To address these issues, this paper proposes a novel Unified Structural Matrix Framework (USMF) for unsupervised feature selection. Specifically, a dynamically learnable, non-negative, symmetric structure matrix is introduced to consistently capture both global and local structural relationships within a single variable. This matrix preserves the global data structure via a trace-maximizing term, similar to weighted principal component analysis, while maintaining local geometric relationships via weighted distance constraints in the embedding space. Furthermore, a Frobenius norm (F-norm) consistency constraint is introduced to preserve neighborhood information and stabilize structure learning. Concurrently, an l2;1-norm regularization is imposed on the projection matrix to achieve effective feature selection. An alternating optimization algorithm is designed to solve the proposed model. Extensive experiments on multiple public datasets demonstrate that USMF outperforms existing state-of-the-art unsupervised feature selection methods in terms of Clustering Accuracy (ACC) and Normalized Mutual Information (NMI).