Abstract
The properties of solvability/regularity of problems and correctness/completeness of algorithmic models are fundamental components of the algebraic approach to pattern recognition. In this paper, we formulate the principles of the metric approach to the data analysis of poorly formalized problems and hence with obtain metric forms of the criteria of solvability, regularity, correctness, and completeness. In particular, the analysis of the compactness properties of metric configurations allowed us to obtain a set of sufficient conditions for the existence of correct algorithms. These conditions can be used for assessment of the quality of the methods of formalization of the problems for arbitrary algorithms and algorithmic models. The general schema proposed for the data analysis of poorly formalized problems includes the criteria in the cross-validation form and can assess not only the quality of formalization, but also the extent of overtraining pertaining to the procedures of generation and selection of feature descriptions.
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Ivan Yur’evich Torshin. Born 1972. Graduated from the Department of Chemistry, Moscow State University, in 1995. Received candidates degrees in chemistry in 1997 and in physics and mathematics in 2011. Currently is an associate professor at Moscow Institute of Physics and Technology, lecturer at the Faculty of Computational Mathematics and Cybernetics, Moscow State University, leading scientist at the Russian Branch of the Trace Elements Institute for UNESCO, and a member of the Center of Forecasting and Recognition. Author of 225 publications in peer-reviewed journals in biology, chemistry, medicine, and informatics and of 3 monographs in the series “Bioinformatics in Post-genomic Era” (Nova Biomedical Publishers, NY, 2006–2009).
Konstantin Vladimirovich Rudakov. Born 1954. Russian mathematician, Full member of the Russian Academy of Sciences, Head of the Department of Computational Methods of Forecasting at the Dorodnicyn Computing Centre, Federal Research Center “Informatics and Control,” Russian Academy of Sciences, and Head of the Chair “Intelligent Systems” at the Moscow Institute of Physics and Technology.
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Torshin, I.Y., Rudakov, K.V. Combinatorial analysis of the solvability properties of the problems of recognition and completeness of algorithmic models. Part 2: Metric approach within the framework of the theory of classification of feature values. Pattern Recognit. Image Anal. 27, 184–199 (2017). https://doi.org/10.1134/S1054661817020110
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DOI: https://doi.org/10.1134/S1054661817020110