A new adaptive elastic loss for robust unsupervised feature selection

Abstract

The sparse-based unsupervised dimension reduction technique has been demonstrated to be an effective tool for dealing with high-dimensional data. Among them, the sparse regularization technique is used to introduce the prior knowledge of the model and helps unsupervised dimension reduction algorithms to complete the feature selection. However, the sparse regularization only considers the sparsity of representation. It ignores the group effect of variables among which the pairwise correlations are very high. To solve these issues, we present a novel regularization approach based on adaptive elastic loss in this study. Then, utilizing the regularization method, an efficient unsupervised feature selection methodology is given. Additionally, we devise an efficient alternative optimization algorithm to resolve the complex optimization issue of our proposed method and conduct a theoretical analysis of its computational complexity and convergence. Eventually, we conduct comprehensive experiments to test the validity of our proposed method, and real-world data and a simulation study demonstrate that our proposed method outperforms many state-of-the-art unsupervised feature selection methods in terms of clustering and classification.