Support Vector Method for Novelty Detection

Suppose you are given some dataset drawn from an underlying probability distributionPand you want to estimate a “simple ” subsetSof input space such that the probability that a test point drawn from P lies outside of Sequals some a priori specified between0and1. We propose a m ethod to approach this problem by trying to estimate a function f which is positive on S and negative on the complement. The functional form offis given by a kernel expansion in terms of a potentially small subset of the training data; it is regularized by controlling the length of the weight vector in an associated feature space. We provide a theoretical analysis of the statistical performance of our algorithm. The algorithm is a natural extension of the support vector algorithm to the case of unlabelled data.