Robust feature selection via simultaneous sapped norm and sparse regularizer minimization

High dimension is one of the key characters of big data. Feature selection, as a framework to identify a small subset of illustrative and discriminative features, has been proved as a basic solution in dealing with high-dimensional data. In previous literatures, ℓ_{2, p}-norm regularization was studied by many researches as an effective approach to select features across data sets with sparsity. However, ℓ_{2, p}-norm loss function is just robust to noise but not considering the influence of outliers. In this paper, we propose a new robust and efficient feature selection method with emphasizing Simultaneous Capped ℓ₂-norm loss and ℓ_{2, p}-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_{2, p}-norm regularization is used to select features across data sets with joint sparsity. An efficient approach is then introduced with proved convergence. Extensive experimental studies on synthetic and real-world datasets demonstrate the effectiveness of our method in comparison with other popular feature selection methods.