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The selection of Gaussian kernel parameters plays an important role in theapplications of support vector classification (SVC). A commonly used method isthe k-fold cross validation with grid search (CV), which is extremelytime-consuming because it needs to train a large number of SVC models. In thispaper, a new approach is proposed to train SVC and optimize the selection ofGaussian kernel parameters. We first formulate the training and parameterselection of SVC as a minimax optimization problem named as MaxMin-L2-SVC-NCH,in which the minimization problem is an optimization problem of finding theclosest points between two normal convex hulls (L2-SVC-NCH) while themaximization problem is an optimization problem of finding the optimal Gaussiankernel parameters. A lower time complexity can be expected in MaxMin-L2-SVC-NCHbecause CV is not needed. We then propose a projected gradient algorithm (PGA)for training L2-SVC-NCH. The famous sequential minimal optimization (SMO)algorithm is a special case of the PGA. Thus, the PGA can provide moreflexibility than the SMO. Furthermore, the solution of the maximization problemis done by a gradient ascent algorithm with dynamic learning rate. Thecomparative experiments between MaxMin-L2-SVC-NCH and the previous bestapproaches on public datasets show that MaxMin-L2-SVC-NCH greatly reduces thenumber of models to be trained while maintaining competitive test accuracy.These findings indicate that MaxMin-L2-SVC-NCH is a better choice for SVCtasks.

MaxMin-L2-SVC-NCH: A Novel Approach for Support Vector Classifier Training and Parameter Selection