Metrics of Algebraic Closures in Pattern Recognition Problems with Two Nonoverlapping Classes

摘要

It is shown that, in the pattern recognition problem with two nonoverlapping classes, thematrices of estimates of the object closeness are described by a metric. The transition to the algebraicclosure of the model of recognizing operators of finite degree corresponds to the application of a specialtransformation of this metric. It is proved that the minimal degree correct algorithm can be found as apolynomial of a special form. A simple criterion for testing classification implementations is obtained.