The One Class Support Vector Machine Solution Path

This paper applies the algorithm of Hastie et al., (2004) to the problem of learning the entire solution path of the one class support vector machine (OC-SVM) as its free parameter ν varies from 0 to 1. The OC-SVM with Gaussian kernel is a nonparametric estimator of a level set of the density governing the observed sample, with the parameter ν implicitly defining the corresponding level. Thus, the path algorithm produces estimates of all level sets and can therefore be applied to a variety of problems requiring estimation of multiple level sets including clustering, outlier ranking, minimum volume set estimation, and density estimation. The algorithm's cost is comparable to the cost of computing the OC-SVM for a single point on the path. We introduce a heuristic for enforced nestedness of the sets in the path, and present a method for kernel bandwidth selection based in minimum integrated volume, a kind of AUC criterion. These methods are illustrated on three datasets.