Support Vector Machine Classifier via L_0/1 Soft-Margin Loss
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Support vector machine (SVM) has attracted great attentions for the last two decades due to its extensive applications, and thus numerous optimization models have been proposed. To distinguish all of them, in this paper, we introduce a new model equipped with an L_0/1 soft-margin loss (dubbed as L_0/1-SVM) which well captures the nature of the binary classification. Many of the existing convex/non-convex soft-margin losses can be viewed as a surrogate of the L_0/1 soft-margin loss. Despite the discrete nature of L_0/1, we manage to establish the existence of global minimizer of the new model as well as revealing the relationship among its minimizers and KKT/P-stationary points. These theoretical properties allow us to take advantage of the alternating direction method of multipliers. In addition, the L_0/1-support vector operator is introduced as a filter to prevent outliers from being support vectors during the training process. Hence, the method is expected to be relatively robust. Finally, numerical experiments demonstrate that our proposed method generates better performance in terms of much shorter computational time with much fewer number of support vectors when against with some other leading methods in areas of SVM. When the data size gets bigger, its advantage becomes more evident.
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