Metrics of algebraic closures in pattern recognition problems with two nonoverlapping classes |
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Authors: | A. G. D’yakonov |
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Affiliation: | (1) Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia |
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Abstract: | It is shown that, in the pattern recognition problem with two nonoverlapping classes, the matrices of estimates of the object closeness are described by a metric. The transition to the algebraic closure of the model of recognizing operators of finite degree corresponds to the application of a special transformation of this metric. It is proved that the minimal degree correct algorithm can be found as a polynomial of a special form. A simple criterion for testing classification implementations is obtained. |
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Keywords: | pattern recognition estimation algorithm matrices of estimates correct algorithm algebra over algorithms metric Gram’ s matrix minimal degree |
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