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Construction of a correct algorithm and Spatial Neural Network for Recognition Problems with Binary Data

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2018年第10期58卷 1673-1686页

作者： Dyusembaev, A. E. Grishko, M. V. Al Farabi Kazakh Natl Univ Alma Ata 050012 Kazakhstan

Conditions under which it is possible to design a correct algorithm and a six-level spatial neural network reproducing the computations performed by this algorithm for recognition problems with binary data (-regular problems) are found. A distinctive feature of this network is the use of diagonal activation functions in its internal layers, which significantly simplify intermediate computations in the inner and outer loops. Given an -regular problem, the network sequentially computes the rows of the classification matrix for the test sample objects. The computational process (i.e., the inner loop) for each test object consists inside the elementary 3-level network (i.e., -block) of a single iteration determined by a single object of the training set. The proposed approach to the neural network construction does not rely on the conventional approach based on the minimization of a functional;rather, it is based on the operator theory developed by Zhuravlev for solving recognition and classification problems.

关键词： correct algorithm neural network -block algebra

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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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Algebra over estimation algorithms: Normalization with respect to the interval

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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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