Robust unsupervised feature selection based on matrix factorization with adaptive loss via bi-stochastic graph regularization

Unsupervised feature selection (UFS) has gained increasing attention and research interest in various domains, such as machine learning and data mining. Recently, numerous matrix factorization-based methods have been widely adopted for UFS. However, the following issues still exist. First, most methods based on matrix factorization use the squared Frobenius-norm to measure the loss term, making them sensitive to outliers. Although using l2,1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \varvec{l}_{\varvec{2,1}} $$\end{document}-norm-based loss improves the robustness, it is sensitive to small loss. Second, most existing matrix factorization-based methods utilize a fixed graph to preserve the local structure of data, making them fail to capture the intrinsic local structure accurately. To address the above drawbacks, we present a novel robust UFS model named matrix factorization with adaptive loss via bi-stochastic graph regularization (MFALBS). Specifically, MFALBS decomposes the projected data points into two orthogonal matrices to facilitate discriminative feature selection. Meanwhile, MFALBS utilizes an adaptive loss function for measuring the loss term in order to enhance model robustness. Moreover, MFALBS adopts an adaptive learning strategy for optimal bi-stochastic graph learning in order to improve local structure preservation ability. Finally, an optimization algorithm is proposed to solve the proposed model. Experimental results on real-world datasets show the effectiveness and superiority of MFALBS.