Efficient and robust feature selection via joint ℓ_2;1-norms minimization

Feature selection is an important component of many machine learning applications. Especially in many bioinformatics tasks, efficient and robust feature selection methods are desired to extract meaningful features and eliminate noisy ones. In this paper, we propose a new robust feature selection method with emphasizing joint ℓ_2;1-norm minimization on both loss function and regularization. The ℓ_2;1-norm based loss function is robust to outliers in data points and the ℓ_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 empirical studies are performed on six data sets to demonstrate the performance of our feature selection method.