COMPUTER IMPLEMENTED METHODS AND SYSTEMS FOR OPTIMAL QUADRATIC CLASSIFICATION SYSTEMS

摘要

A computer-implemented method for quadratic classification involves generating a data-driven likelihood ratio test based on a dual locus of likelihoods and principal eigenaxis components that contains Bayes' likelihood ratio and automatically generates the best quadratic decision boundary. A dual locus of likelihoods and principal eigenaxis components, formed by a locus of weighted reproducing kernels of extreme points, satisfies fundamental statistical laws for a quadratic classification system in statistical equilibrium and is the basis of an optimal quadratic system for which the eigenenergy and the Bayes' risk are minimized, so that the classification system achieves Bayes' error rate and exhibits optimal generalization performance. Quadratic classification systems can be linked with other such systems to perform multiclass quadratic classification and to fuse feature vectors from different data sources. Quadratic classification systems also provide a practical statistical gauge that measures data distribution overlap and Bayes' error rate.