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01-07-2019 | MATHEMATICAL METHOD IN PATTERN RECOGNITION | Issue 3/2019

Pattern Recognition and Image Analysis 3/2019

On a Classification Method for a Large Number of Classes

Journal:
Pattern Recognition and Image Analysis > Issue 3/2019
Authors:
Yu. I. Zhuravlev, V. V. Ryazanov, L. H. Aslanyan, H. A. Sahakyan
Important notes
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Yurii Ivanovich Zhuravlev. Born 1935. Graduated from Moscow State University in 1957. Received doctoral degree in 1965, Professor since 1967, and Academician of the Russian Academy of Sciences since 1992. Currently Deputy Director of the Dorodnitsyn Computing Centre, Federal Research Center “Informatics and Control,” Russian Academy of Sciences, deputy academic secretary at the Chair at the Mathematics Department of the Russian Academy of Sciences, and Head of Chair at Moscow State University. Editor-in-Chief of Pattern Recognition and Image Analysis. Foreign member of the Spanish Royal Academy of Sciences, the National Academy of Sciences of Ukraine, and the European Academy of Sciences. Winner of the Lenin and Lomonosov Prizes. Author of 257 publications. There are more than 100 candidates of sciences and 26 doctors of sciences among his students. Scientific interests: mathematical logic; control systems theory; mathematical theory of pattern recognition, image analysis, and forecasting; operations research; and artificial intelligence.
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Vasilii Vladimirovich Ryazanov. Born 1991. Graduated from Moscow Institute of Physics and Technology (State University) in 2014. Currently is an assistant at the Chair of Informatics and Computational Mathematics at MIPT. Author of 15 publications. Scientific interests: machine learning, pattern recognition, neural networks, forecasting, incomplete data, and multiclass classification.
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Levon Hakopovich Aslanyan. Graduated from Novosibirsk State University. Received candidates degree in 1976 and doctoral degree in 1997. Professor since 1997. Currently is Head of Department of Discrete Mathematics at the Institute for Informatics and Automation Problems, National Academy of Sciences of the Republic of Armenia. Scientific interests: mathematical logic, discrete mathematics, mathematical theory of recognition, and artificial intelligence.
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Hasmik Artemovna Sahakyan. Graduated from Yerevan State University. Received candidates degree in 2002 and doctoral degree in 2018. Currently is scientific secretary at the Institute for Informatics and Automation Problems, National Academy of Sciences of the Republic of Armenia, and a leading researcher at the Department of Discrete Mathematics. Scientific interests: combinatorics, discrete tomography, and data mining.
Translated by I. Nikitin

Abstract

The construction of a two-level decision scheme for recognition problems with many classes is proposed that is based on the development of the error-correcting output codes (ЕСОС) method. In the “classical” ЕСОС, a large number of partitions of the original classes into two macroclasses are constructed. Each macroclass is a union of some original classes. Each macroclass is assigned either 0 or 1. As a result, each original class is defined by a row of 0 and 1 (the stage of encoding) and a coding matrix is constructed. The stage of classification of an arbitrary new object consists in the solution of each dichotomic problem and application of a special decision rule (the stage of decoding). In this paper, new methods for weighting and taking into account codewords, modifying decision rules, and searching for locally optimal dichotomies are proposed, and various quality criteria for classification and the cases of extension of a codeword are considered.

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