2020•Doklady MathematicsRequires access

Completeness Criteria for a Linear Model of Classification Algorithms with Respect to Families of Decision Rules

A. G. D’yakonov, А. М. Головина

Abstract

Abstract In the framework of Zhuravlev’s algebraic approach to classification problems, a linear model of algorithms is investigated (estimates of class membership are generated by linear regressions). The possibility of weakening the completeness requirement (obtaining an arbitrary estimation matrix) in order to obtain any classification of a fixed set of objects by using special decision rules is investigated.

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Key concepts: Completeness (order theory), Mathematics, Algebraic number, Class (philosophy), Set (abstract data type), Algorithm, Matrix (chemical analysis), Algebra over a field