Abstract
A problem of classification by precedents in partial precedence models is considered. An algorithm is presented for searching for maximum logical regularities of a class (LRCs) for consistent training tables. A two-level solution scheme of a problem is proposed for finding an optimal decision rule. First, LRCs are obtained by training data, and a mapping of the initial feature descriptions of objects into a space of points of a discrete unit cube is constructed. The objects of the training sample can be divided by a hyperplane in the latter space. It is suggested that a linear decision rule in the latter space that provides the maximum gap, similar to the support vector method, should be used as the decision rule.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. N. Dmitriev, Yu. I. Zhuravlev, and F. P. Krendelev, “On mathematical principles for classifying objects and phenomena,” in Discrete Analysis. Collection of Papers (Inst. Math. Siberian Branch of the USSR Acad. Sci., Novosibirsk, 1966), Issue 7, pp. 3–11 [in Russian].
Yu. I. Zhuravlev and V. V. Nikiforov, “Recognition algorithms based on estimations calculation,” Kibernetika, No. 3, 1–11 (1971).
L. V. Baskakova and Yu. I. Zhuravlev, “A model of recognizing algorithms with representative sets and systems of reference sets,” Zh. Vychisl. Mat. Mat. Fiz. 21(5), 1264–1275 (1981).
V. V. Ryazanov, “Logical regularities in recognition problems (parametrical approach),” Zh. Vychisl. Mat. Mat. Fiz. 47(10), 1793–1808 (2007).
O. V. Sen’ko, “The way to use weighted voting according to base sets in recognition problems,” Zh. Vychisl. Mat. Mat. Fiz. 35(10), 1552–1563 (1995).
N. V. Kovshov, V. L. Moiseev, and V. V. Ryazanov, “Algorithms for searching logical regularities in recognition problems,” Zh. Vychisl. Mat. Mat. Fiz. 48(2), 329–344 (2008).
J. C. Christopher and A. Burges, “Tutorial on support vector machines for pattern recognition appeared,” Data Mining Knowledge Discovery 2, 121–167 (1998).
A. Asuncion and D. J. Newman, UCI Machine Learning Repository. http://www.ics.uci.edu/~mlearn/MLRepository.html
Author information
Authors and Affiliations
Corresponding author
Additional information
Yurii Ivanovich Zhuravlev. Born 1935. Graduated from the Moscow State University in 1957. Received doctoral degree in 1965, is Professor since 1967, and Academician of the Russian Academy of Sciences since 1992. Currently is Deputy Director of the Dorodnicyn Computing Centre, Russian Academy of Sciences, Chair at the Mathematics Department of the Russian Academy of Sciences, Deputy Academician Secretary at the Division of Mathematical Sciences, 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. Scientific interests: mathematical logic; control systems theory; mathematical theory of pattern recognition, image analysis, and forecasting; operations research; and artificial intelligence.
Levon Akopovich Aslanyan. Born 1945. Graduated from the Novosibirsk State University in 1968. Received candidate’s degree in 1976 and doctoral degree in 1997. Currently is Head of the Department of Discrete Simulation, Analysis, and Recognition Technologies 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.
Vladimir Vasil’evich Ryazanov. Born 1950. Graduated from the Moscow Institute of Physics and Technology in 1973. Received candidate’s degree in 1977 and doctoral degree in 1994. Academician of the Russian Academy of Natural Sciences since 1996 and Professor since 2008. Since 1976 has been with the Dorodnicyn Computing Centre, Russian Academy of Sciences. Currently is Head of the Department of Mathematical Problems of Recognition and Methods of Combinatorial Analysis. Scientific interests: mathematical theory of recognition, cluster analysis, data analysis, optimization of recognition models, artificial intellect, and applied systems of analysis and recognition.
Rights and permissions
About this article
Cite this article
Zhuravlev, Y.I., Aslanyan, L.A. & Ryazanov, V.V. Analysis of a training sample and classification in one recognition model. Pattern Recognit. Image Anal. 24, 347–352 (2014). https://doi.org/10.1134/S1054661814030183
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1054661814030183