Adaptive huberized support vector machine and its application to microarray classification

This paper proposes an adaptive huberized support vector machine for simultaneous classification and gene selection. By introducing the data-driven weights, the proposed support vector machine can adaptively identify the important genes in groups, thus encouraging an adaptive grouping effect. Furthermore, the shrinkage biases for the coefficients of important genes are largely reduced. A reasonable correlation between the two regularization parameters is also given, based on which the solution paths are shown to be piecewise linear with respect to the single regularization parameter. Experiment results on leukaemia data set are provided to illustrate the effectiveness of the proposed method.