Duke University

presents:

Craig Cooley

Ohio State University

"An Alternative Approach to Nonparametric
Kernel Classification"

Abstract:

As an alternative to Fisher's linear and quadratic discriminant functions, multivariate kernel density estimation is often used as the basis for a nonparametric classification technique. The advantage of the kernel approach is one of increased generality in the form of the class-conditional densities that can be consistently estimated. However, the multivariate kernel classifier suffers from the curse of dimensionality, requiring inordinately large sample sizes to achieve a reasonable degree of accuracy in high-dimensional settings. A different approach to kernel classification can be motivated through an alternative interpretation of linear and quadratic discriminant analysis in which rotations of the coordinate axes are employed to obtain an assumed mutual independence between the components of the rotated data. Post rotation, a multivariate density estimator can be computed as a product of univariate kernel density estimators and subsequently transformed back to the original coordinate space. Conditional on known transformation and an independence assumption, this kernel density product (KDP) estimator has a significantly faster rate of decline of mean integrated squared error than multivariate kernel estimation. A classifier based on kernel density products satisfies consistency properties in problems for which the independence assumption holds. The method performs well in a variety of examples, including a 20 dimensional target recognition problem.

February 23, 1996

11:45 am - 12:45 pm

130 Sociology/Psychology Building

Any questions concerning the seminar may be addressed to Cheryl McGhee @[919] 684-8029, e-mail cheryl@stat.duke.edu, or finger seminar@stat.duke.edu