Quantification of pattern recognition quality by multivariate normal distribution functions

Abstract

Analysis of the multivariate data distributions can be helpful or directly applicable in pattern recognition tests. Estimate of the volume of the critical region of overlapping distributions is essential in determination of the confidence level of classification. Mathematical tools for analysis of the multivariate distributions (included probability, false positives and false negatives, means for calculation of the critical region) are developed. Sum of the false negative and the false positive is found as a very approximate characteristic of the total uncertainty of classification. The false negative probability is extremely distribution coordinate dependent and analysis of the details of the overlapping distributions is needed to evaluate the real risk of misclassification of samples. Application of the multivariate distributions to the regional classification of wine samples according to the data of multielement analysis is presented as an example.