Choosing the Parameters of 2-norm Soft Margin Support Vector Machines According to the Cluster Validity

Abstract

Determining the kernel and error penalty parameters for support vector machines (SVMs) is very problem-dependent in practice. This paper proposes using a cluster validation index in the feature space to help choose parameters for training 2-norm soft margin support vector machines. With the proposed method, the kernel parameters and the penalty parameter of the error term in the 2-norm soft margin SVM are considered to be the parameters of an alternative kernel for a hard margin SVM. Thus the values of cluster validation index can be calculated in the feature spaces which are defined by the kernels with the parameters. The cluster validation index shows whether the data are well-separated in a feature space, so it can be used to determine whether a combination of the kernel parameters leads to a feature space in which the data are easy to be classified. It guides the search of parameters toward a good testing accuracy, so the search range of the parameters is confined to a small region, and the parameters selecting time of the SVM training process can be shortened.