The design of a nonparametric hierarchical classifier

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