The design of a nonparametric hierarchical classifier

Abstract

The authors propose a method based on kernel density estimates to partition sequentially the feature space along the best feature axis (either one of the original axes or one obtained by a carefully developed one-dimensional linear feature transformation). This method alleviates the storage and classification speed problems of traditional kernel-based classifiers without losing their flexibility and their relative insensitivity to dimensionality. The authors present a simple procedure and a distribution-free criterion for finding a good smoothing parameter for the kernel density estimate and develop a one-dimensional feature linear transformation based on correlation between density functions, which can be applied regardless of the geometrical structure of the data. The authors' proposals are validated by theoretical results and by simulations. An application to the severely under-sampled problem of texture classification (only 32 design samples per class in 22-dimensional space) is presented.<>