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Simultaneous feature selection and classification have been explored in the literature to extend the support vector machine (SVM) techniques by adding penalty terms to the loss function directly. However, it is the kernel function that controls the performance of the SVM, and an imbalance in the data will deteriorate the performance of an SVM. In this paper, we examine a new method of simultaneous feature selection and binary classification. Instead of incorporating the standard loss function of the SVM, a penalty is added to the data-adaptive kernel function directly to control the performance of the SVM, by firstly conformally transforming the kernel functions of the SVM, and then re-conducting an SVM classifier based on the sparse features selected. Both convex and non-convex penalties, such as least absolute shrinkage and selection (LASSO), moothly clipped absolute deviation (SCAD) and minimax concave penalty (MCP) are explored, and the oracle property of the estimator is established accordingly. An iterative optimization procedure is applied as there is no analytic form of the estimated coefficients available. Numerical comparisons show that the proposed method outperforms the competitors considered when data are imbalanced, and it performs similarly to the competitors when data are balanced. The method can be easily applied in medical images from different platforms.

Simultaneous Feature Selection and Classification for Data-Adaptive Kernel-Penalized SVM