On the Use of Adaptive Weights for the F_infty-Norm Support Vector Machine

초록

When the input features are generated by factors in a classification problem, it is more meaningful to identify important factors, rather than individual features. The $F_{\infty }$-norm support vector machine(SVM) has been developed to perform automatic factor selection in classification. However, the $F_{\infty }$-norm SVM may suffer from estimation inefficiency and model selection inconsistency because it applies the same amount of shrinkage to each factor without assessing its relative importance. To overcome such a limitation, we propose the adaptive $F_{\infty }$-norm (${\text{AF}}_{\infty }$-norm) SVM, which penalizes the empirical hinge loss by the sum of the adaptively weighted factor-wise $L_{\infty }$-norm penalty. The ${\text{AF}}_{\infty }$-norm SVM computes the weights by the 2-norm SVM estimator and can be formulated as a linear programming(LP) problem which is similar to the one of the $F_{\infty }$-norm SVM. The simulation studies show that the proposed ${\text{AF}}_{\infty }$-norm SVM improves upon the $F_{\infty }$-norm SVM in terms of classification accuracy and factor selection performance.

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