Double-Structured Sparsity Guided Flexible Embedding Learning for Unsupervised Feature Selection

In this article, we propose a novel unsupervised feature selection model combined with clustering, named double-structured sparsity guided flexible embedding learning (DSFEL) for unsupervised feature selection. DSFEL includes a module for learning a block-diagonal structural sparse graph that represents the clustering structure and another module for learning a completely row-sparse projection matrix using the $\ell_{2,0}$ -norm constraint to select distinctive features. Compared with the commonly used $\ell_{2,1}$ -norm regularization term, the $\ell_{2,0}$ -norm constraint can avoid the drawbacks of sparsity limitation and parameter tuning. The optimization of the $\ell_{2,0}$ -norm constraint problem, which is a nonconvex and nonsmooth problem, is a formidable challenge, and previous optimization algorithms have only been able to provide approximate solutions. In order to address this issue, this article proposes an efficient optimization strategy that yields a closed-form solution. Eventually, through comprehensive experimentation on nine real-world datasets, it is demonstrated that the proposed method outperforms existing state-of-the-art unsupervised feature selection methods.