Heterogeneous space co-sparse representation: Leveraging fuzzy dependency and feature reconstruction for feature selection

Feature selection is an efficient approach to dimensionality reduction. There is a large number of literatures tackling this issue. Most of them prioritize classification ability of features, but often fail to fully consider the synergistic effect of local and global subspace information, thus limit the performance of feature selection in revealing the intrinsic structure of data. In this paper, a novel embedded feature selection model, called the heterogeneous space collaborative sparse representation for feature selection through leveraging fuzzy dependency and feature reconstruction (HCoSRDC), is proposed. In the proposed model, a fuzzy self-information operator is constructed to nonlinearly map samples from their feature space to a fuzzy dependency space, where the fuzzy dependency discloses classification ability of features and the local subspace structure in data is captured. Furthermore, samples are sparsely self-represented in their feature reconstruction space to extract global subspace structure while emphasizing feature distinctiveness. The consistency between local sparse representation and global sparse representation is integrated to learn weights of features for feature selection. An algorithm is designed to solve HCoSRDC. Extensive experiments on various benchmark datasets are conducted and experimental results demonstrate the superior performance of the proposed model in comparison with the state-of-the-art models for feature selection.