Geodesic
Metrics of algebraic closures in pattern recognition problems with two nonoverlapping classes
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 5, pp. 916-927

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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. 
@article{ZVMMF_2008_48_5_a12,
     author = {A. G. D'yakonov},
     title = {Metrics of algebraic closures in pattern recognition problems with two nonoverlapping classes},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {916--927},
     publisher = {mathdoc},
     volume = {48},
     number = {5},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_5_a12/}
}
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A. G. D'yakonov. Metrics of algebraic closures in pattern recognition problems with two nonoverlapping classes. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 5, pp. 916-927. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_5_a12/