Classification via kernel product estimators

Multivariate kernel density estimation is often used as the basis for a non parametric classification technique. However, the multivariate kernel class ifier suffers from the curse of dimensionality, requiring inordinately larg e sample sizes to achieve a reasonable degree of accuracy in high dimension al settings. A variance stabilising approach to kernel classification can b e motivated through an alternative interpretation of linear and quadratic d iscriminant analysis in which rotations of the coordinate axes are employed to obtain an assumed mutual independence among the components of the rotat ed data. This alternative method, which we call the method of kernel produc t estimators, performs well in a variety of examples, including a 20-dimens ional target recognition problem.