Average classification accuracy over collections of gaussian problems—common covariance matrix case

摘要

The mean probability of correct classification (Pcr) is calculated over a collection of equiprobable two-class Gaussian problems with a common covariance matrix for each problem. The Bayes minimum error classification rule, in which the unbiased estimates of the mean vectors and covariance matrices are used in place of the true values, is the classification rule considered. The variation of Pcr with the dimensionality N is investigated for three interesting cases with different complexities. In the first case all the parameters of the class-conditional densities are known. For the second case the common covariance matrix is assumed known and only the mean vectors need to be estimated, while all the parameters need to be estimated in the last case. For these three cases the relationship between Pcr and N is plotted for a specific collection of problems. For the case of finite sample size, peaking of Pcr with N is encountered in most of the cases considered.