Expected error of minimum empirical error and maximal margin classifiers

This paper compares two linear nonparametric classification algorithms-zero empirical error classifier and maximum margin classifier with parametric linear classifiers designed by using assumptions that pattern classes are multivariate Gaussian. Analytical formulae and a table for the mean expected probability of misclassification EP_N are presented and show the classification error is mainly determined by N/p, a learning set size/dimensionality ratio. However an influence of the learning sample size on generalization error of parametric and nonparametric linear classifiers is totally different. It is shown that the nonparametric approach to design the linear classifier allows to obtain reliable rules even in cases when the number of features is significantly larger than the number of training vectors