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algebra over estimation algorithms: Normalization with respect to the interval

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2009年第1期49卷 194-202页

作者： D'yakonov, A. G. Moscow MV Lomonosov State Univ Fac Computat Math & Cybernet Moscow 119992 Russia

algebra over estimation algorithms with addition, multiplication by a constant, and normalization operations is investigated. Normalization is interpreted as a linear (with respect to each row) transformation of the matrix of estimates that takes the maximum entry of the row to unity and the minimum entry to zero. The algebraic closure is described, a formula for its dimension is obtained, and correctness criteria are formulated.

关键词： pattern recognition estimation algorithm matrices of estimates correct algorithm normalization algebra over algorithms

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algebra over estimation algorithms: Normalization and division

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Computational Mathematics and Mathematical Physics 2007年第6期47卷 1050-1060页

作者： D'yakonov A.G. Faculty of Computational Mathematics and Cybernetics Moscow State University Leninskie gory Moscow 119992 Russian Federation

An algebra over recognition algorithms supplemented with a normalization operation (under various definitions) and the division operation is investigated. Correctness criteria for various algebraic closures are obtain... 详细信息

关键词： algebra over algorithms Correct algorithm Division of algorithms Estimation algorithm Matrices of estimates Normalization Pattern recognition

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

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2008年第5期48卷 866-876页

作者： D'yakonov, A. G. Moscow MV Lomonosov State Univ Fac Computat Math & Cybernet Moscow 119992 Russia

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.

关键词： pattern recognition estimation algorithm matrices of estimates correct algorithm algebra over algorithms metric Gram's matrix minimal degree

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Theory of equivalence systems for describing algebraic closures of a generalized estimation model. II

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2011年第3期51卷 490-504页

作者： D'yakonov, A. G. Moscow MV Lomonosov State Univ Fac Computat Math & Cybernet Moscow 119991 Russia

Characteristic matrices and metrics of equivalence systems are studied that help give an efficient description of conjunctions of equivalence systems. Using these results, families of correct polynomials in the algebr... 详细信息

关键词： pattern recognition classification estimation algorithms algebraic approach algebraic closure algebra over algorithms correctness equivalence metric

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Theory of Equivalence Systems for Describing the algebraic Closures of a Generalized Estimation Model

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2010年第2期50卷 369-381页

作者： D'yakonov, A. G. Moscow MV Lomonosov State Univ Fac Computat Math & Cybernet Moscow 119992 Russia

The recognition problem is considered in which the initial information is given by the values of similarity functions on pairs of objects. A generalization of the estimation algorithm model for this problem is proposed. A theory for the description and analysis of algebraic closures of the generalized and classical models is developed.

关键词： pattern recognition classification estimation algorithms algebraic approach algebraic closure algebra over algorithms correctness equivalence

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