Borderline detection by Bayes vector quantizers

Borderline detection is the problem of finding samples falling near the decision boundary. It has many applications, related to the fact that for these samples small variations of feature values, due for instance to the presence of noise, can completely change their classification. In this paper, we propose an approach to borderline detection based on the geometric characteristics of labeled vector quantizers. The approach is based on the estimation of the true decision boundary by means of the Bayes Vector Quantizer (BVQ) algorithm. BVQ is a stochastic gradient algorithm for the minimization of the misclassification risk, hence it guarantees the accurate approximation of the optimal decision boundary. The features of the approach are discussed in comparison with Support Vector Machines (SVM), that is the best boundary hunting technique known in the literature.