MaxMin-L2-SVC-NCH: A New Method to Train Support Vector Classifier with the Selection of Model's Parameters

Abstract

The selection of model's parameters plays an important role in the application of support vector classification (SVC). The commonly used method of selecting model's parameters is the k-fold cross validation with grid search (CV). It is extremely time-consuming because it needs to train a large number of SVC models. In this paper, a new method is proposed to train SVC with the selection of model's parameters. Firstly, training SVC with the selection of model's parameters is modeled as a minimax optimization problem (MaxMin-L2-SVC-NCH), in which the minimization problem is an optimization problem of finding the closest points between two normal convex hulls (L2-SVC-NCH) while the maximization problem is an optimization problem of finding the optimal model's parameters. A lower time complexity can be expected in MaxMin-L2-SVC-NCH because CV is abandoned. A gradient-based algorithm is then proposed to solve MaxMin-L2-SVC-NCH, in which L2-SVC-NCH is solved by a projected gradient algorithm (PGA) while the maximization problem is solved by a gradient ascent algorithm with dynamic learning rate. To demonstrate the advantages of the PGA in solving L2-SVC-NCH, we carry out a comparison of the PGA and the famous sequential minimal optimization (SMO) algorithm after a SMO algorithm and some KKT conditions for L2-SVC-NCH are provided. It is revealed that the SMO algorithm is a special case of the PGA. Thus, the PGA can provide more flexibility. The comparative experiments between MaxMin-L2-SVC-NCH and the classical parameter selection models on public datasets show that MaxMin-L2-SVC-NCH greatly reduces the number of models to be trained and the test accuracy is not lost to the classical models. It indicates that MaxMin-L2-SVC-NCH performs better than the other models. We strongly recommend MaxMin-L2-SVC-NCH as a preferred model for SVC task