Hierarchically penalized support vector machine with grouped variables

When input features are naturally grouped or generated by factors in a linear classification problem, it is more meaningful to identify important groups or factors rather than individual features. The F ∞ -norm support vector machine (SVM) and the group lasso penalized SVM have been developed to perform simultaneous classification and factor selection. However, these group-wise penalized SVM methods may suffer from estimation inefficiency and model selection inconsistency because they cannot perform feature selection within an identified group. To overcome this limitation, we propose the hierarchically penalized SVM (H-SVM) that not only effectively identifies important groups but also removes irrelevant features within an identified group. Numerical results are presented to demonstrate the competitive performance of the proposed H-SVM over existing SVM methods.