Efficient and robust feature selection via joint ℓ2,1-norms minimization

Feature selection is an important component of many machine learning applica-tions. Especially in many bioinformatics tasks, efficient and robust feature se-lection methods are desired to extract meaningful features and eliminate noisy ones. In this paper, we propose a new robust feature selection method with em-phasizing joint `2,1-norm minimization on both loss function and regularization. The `2,1-norm based loss function is robust to outliers in data points and the `2,1-norm regularization selects features across all data points with joint sparsity. An efficient algorithm is introduced with proved convergence. Our regression based objective makes the feature selection process more efficient. Our method has been applied into both genomic and proteomic biomarkers discovery. Extensive empir-ical studies are performed on six data sets to demonstrate the performance of our feature selection method.