Multiscale classification using nearest neighbor density estimates

Abstract

Density estimates based on k-nearest neighbors have useful applications in nonparametric discriminant analysis. In classification problems, optimal values of k are usually estimated by minimizing the cross-validated misclassification rates. However, these cross-validation techniques allow only one value of k for each population density estimate, while in a classification problem, the optimum value of k for a class may also depend on its competing population densities. Further, it is computationally difficult to minimize the cross-validated error rate when there are several competing populations. Moreover, in addition to depending on the entire training data set, a good choice of k should also depend on the specific observation to be classified. Therefore, instead of using a single value of k for each population density estimate, it is more useful in practice to consider the results for multiple values of k to arrive at the final decision. This paper presents one such approach along with a graphical device, which gives more information about classification results for various choices of k and the related statistical uncertainties present there. The utility of this proposed methodology has been illustrated using some benchmark data sets.