Classification via kernel product estimators

Multivariate kernel density estimation is often used as the basis for a nonparametric classification technique. 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 variance stabilising 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 among the components of the rotated data. This alternative method, which we call the method of kernel product estimators, performs well in a variety of examples, including a 20-dimensional target recognition problem.