Outlier-Robust Feature Selection with ℓ2, 1-Norm Minimization and Group Row-Sparsity Induced Constraints

Abstract

In the realm of high-dimensional data analysis, the existence of outliers presents a substantial hurdle to the efficacy of feature selection methods that rely on the assumption of Gaussian distribution. To tackle this issue, we propose an outlier-robust feature selection method, ORFS, which combines robust ℓ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</inf>-norm minimization with group row-sparsity induced constrains to achieve both robustness and discriminative prediction capabilities. Moreover, the group row-sparsity constraints subspace learning based on ℓ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,0</inf>-norm can directly select features without parameter tuning. Finally, we introduce an iterative optimization strategy to solve NP-hard problem, and extensive experiments demonstrate the efficacy of ORFS in effectively eliminating the impact of outliers and significantly improving classification performance.