Abstract Recently, exclusive lasso has demonstrated its promising results in selecting discriminative features for each class. The sparsity is enforced on each feature across all the classes via `1,2-norm. However, the exclusive sparsity of `1,2-norm could not screen out a large amount of irrelevant and redundant noise features in high-dimensional data space, since each feature belongs to at least one class. Thus, in this paper, we introduce a novel regularization called “exclusive `2,1”, which is short for “`2,1 with exclusive lasso”, towards robust flexible feature selection. The exclusive `2,1 regularization is the mix of `2,1-norm and `1,2-norm, which brings out joint sparsity at inter-group level and exclusive sparsity at intra-group level simultaneously. An efficient augmented Lagrange multipliers based optimization algorithm is proposed to iteratively solve the exclusive `2,1 regularization in a row-wise fashion. Extensive experiments on twelve benchmark datasets demonstrate the effectiveness of the proposed regularization and the optimization algorithm as compared to state-of-the-arts