A distribution-free geometric upper bound for the probability of error of a minimum distance classifier

摘要

An upperbound to the probability of error per class in a multivariate pattern classification is derived. The bound, given by P(E|class wi)≤NR2i is derived with minimal assumptions; specifically the mean vectors exist and are distinct and the covariance matrices exist and are non-singular. No other assumptions are made about the nature of the distributions of the classes. In equation (i) N is the number of features in the feature (vector) space and Ri is a measure of the “radial neighbourhood” of a class. An expression for Ri is developed. A comparison to the multivariate Gaussian hypothesis is presented.