Robust feature selection via simultaneous capped ℓ2-norm and ℓ2,1-norm minimization

Abstract

High dimension is one of the key characters of big data. Feature selection plays a significant role in many machine learning applications dealing with high-dimensional data. To improve the robustness of feature selection, we propose a new robust feature selection method with emphasizing Simultaneous Capped ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm loss and ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</sub> -norm regularizer Minimization (SCM). The capped ℓ2-norm based loss function can effectively eliminate the influence of noise and outliers in regression and the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</sub> -norm regularization is used to select features across data sets with joint sparsity. Meanwhile, we propose an effective approach to solve the formulated minimization problem. Experimental studies on real-world data sets demonstrate the effectiveness of our method in comparison with other popular feature selection methods.