We discuss the relation betweenɛ-support vector regression (ɛ-SVR) and v -support vector regression ( v -SVR). In particular, we focus on properties that are different from those of C -support vector classification ( C -SVC) and v -support vector classification ( v -SVC). We then discuss some issues that do not occur in the case of classification: the possible range of ɛ and the scaling of target values. A practical decomposition method for v -SVR is implemented, and computational experiments are conducted. We show some interesting numerical observations specific to regression.

The ν-support vector machine (ν-SVM) for classification proposed by Schölkopf, Smola, Williamson, and Bartlett (2000) has the advantage of using a parameter ν on controlling the number of support vectors. In this article, we investigate the relation between ν-SVM and C -SVM in detail. We show that in general they are two different problems with the same optimal solution set. Hence, we may expect that many numerical aspects of solving them are similar. However, compared to regular C -SVM, the formulation of ν-SVM is more complicated, so up to now there have been no effective methods for solving large-scale ν-SVM. We propose a decomposition method for ν-SVM that is competitive with existing methods for C -SVM. We also discuss the behavior of ν-SVM by some numerical experiments.