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Feature selection with specific multivariate performance measures is the key to the success of many applications such as image retrieval and text classification. The existing feature selection methods are usually designed for classification error. In this paper, we propose a generalized sparse regularizer. Based on the proposed regularizer, we present a unified feature selection framework for general loss functions. In particular, we study the novel feature selection paradigm by optimizing multivariate performance measures. The resultant formulation is a challenging problem for high-dimensional data. Hence, a two-layer cutting plane algorithm is proposed to solve this problem, and the convergence is presented. In addition, we adapt the proposed method to optimize multivariate measures for multiple-instance learning problems. The analyses by comparing with the state-of-the-art feature selection methods show that the proposed method is superior to others. Extensive experiments on large-scale and high-dimensional real-world datasets show that the proposed method outperforms l1-SVM and SVM-RFE when choosing a small subset of features, and achieves significantly improved performances over SVMperl in terms of F1-score.