New formulation of SVM for model selection

Model Selection for Support Vector Machines concerns the tuning of SVM hyperparameters; as C controlling the amount of overlap and the kernel parameters. Several criteria developed for tuning the SVM hyperparameters, may not be differentiable w.r.t. C, consequently, gradient-based optimization methods are not applicable. In this paper, we propose a new formulation for SVM that makes possible to include the hyperparameter C in the definition of the kernel parameters. Then, tuning hyperparameters for SVM is equivalent to choosing the best values of kernel parameters. We tested this new formulation for model selection by using the criterion of empirical error, technique based on generalization error minimization through a validation set. The experiments on different benchmarks show promising results confirming our approach.