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Metric correctness of pairwise comparisons in intelligent data analysis

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Języki publikacji
EN
Abstrakty
EN
In modern data analysis and machine learning, data are often represented in the form of pairwise comparisons of the elements of the data set. The pairwise comparisons immediately correspond to the similarity or dissimilarity of objects under investigation, and such a situation regularly arises in the domains of image and signal analysis, bioinformatics, expert evaluation, etc. The practical pairwise comparison functions may be incorrect in terms of potentially using them as scalar products or distances. In contrast to other approaches, we develop in this paper a technique based on the so-called metric approach, which proposes to modify the values of empirical functions so as to get scalar products or distances. The methods for obtaining the correct matrices of pairwise comparisons and for improving their conditionality are developed here.
Słowa kluczowe
Rocznik
Strony
291--334
Opis fizyczny
Bibliogr. 27 poz., rys., tab.
Twórcy
  • Tula State University, Tula, Russia
Bibliografia
  • Aizerman, M. A., Braverman, E. M. and Rozonoer, L. I. (1970) The Method of Potential Functions in Machine Learning Theory [in Russian]. Nauka, Moscow.
  • Bishop, R. L. and Crittenden, R. J. (1964) Geometry of Manifolds. Academic Press, NY.
  • Boyd, S., Ghaoui, L., Feron, E. and Balakrishnan, V. (1994) Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia.
  • Cox, T. F. and Cox, M. A. A. (2001) Multidimensional Scaling. Chapman & Hall/CRC.
  • Dvoenko, S. D. (2009) Clustering and separating of a set of members in terms of mutual distances and similarities. Trans. on MLDM. IBaI Publishing, 2(2), 80–99.
  • Dvoenko, S. D. and Pshenichny, D. O. (2018) On metric correction and conditionality of raw featureless data in machine learning. Pattern Recognit. Image Anal. 28, 595–604. https://doi.org/10.1134/S1054661818040089
  • Dvoenko, S. D. and Pshenichny, D. O. (2021) Rank aggregation based on new types of the Kemeny’s Median. Pattern Recognit. Image Anal. 31, 185–196. https://doi.org/10.1134/S1054661821020061
  • Dvoenko, S. (2022) Clustering of data represented by pairwise comparisons. Control and Cybernetics. 51(3) 343–387. https://doi.org/10.2478/candc-2022-0021
  • Duda R. O. and Hart P. E. (1973) Pattern Classification and Scene Analysis. Wiley, NY.
  • Fisher, R. A. (1936) The use of multiple measurements in taxonomic problems. Annals of Eugenics. 7, 179–188.
  • Gazprom (2000) http://www.bastion.ru/research/am/economy/Harman, H. H. (1976) Modern Factor Analysis. Univ. of Chicago Press, Chicago.
  • Horn, R. and Johnson, C. (1990) Matrix Analysis. Cambridge University Press.
  • Kalyaev, I. A., Levin, I. I., Semernikov, E. A. and Shmoilov, V. I. (2012) Reconfigurable Multipipeline Computing Structures. Nova Science Publishers, Inc. USA.
  • Kemeny, J. and Snell, J. (1963) Mathematical Models in the Social Sciences. Blaisdell, New York.
  • Kozinets, B. N. (1973) A recurrent algorithm for separating convex hulls of two sets. Pattern recognition learning algorithms [in Russian], V. N. Vapnik, editor. Soviet Radio, Moscow, 43–50.
  • Luce, R. D. (1959) Individual Choice Behavior: A Theoretical Analysis. Wiley, NY.
  • Litvak, B. G. (1982) Expert Information: Methods of Acquisition and Analysis [in Russian]. Radio i Svyaz, Moscow.
  • Mirkin, B. G. (1974) A Group Choice Problem [in Russian]. Nauka, Moscow.
  • Nebylitsyn, V. D. (1990) Selected Psychological Proceedings [in Russian]. Pedagogika, Moscow.
  • Pekalska, E. and Duin, R. P. W. (2005) The Dissimilarity Representation for Pattern Recognition. Foundations and Applications. World Scientific, Singapore.
  • Torgerson, W. S. (1958) Theory & Methods of Scaling. Wiley, NY.
  • Tou, J. T. and Gonzalez, R. C. (1977) Pattern Recognition Principles. Addison-Wesley.
  • Vapnik, V. N. and Chervonenkis, A. Y. (1974) Pattern Recognition Theory [in Russian]. Nauka, Moscow.
  • Vapnik, V. N. (1998) Statistical Learning Theory. Adaptive and Learning Systems. Wiley, NY.
  • Young, G. and Householder, A. S. (1938) Discussion of a set of points in terms of their mutual distances. Psychometrika. 3(1). 19–22. https://doi.org/10.1007/BF02287916
  • Zagoruiko, N. G. (1999) Applied Methods of Data and Knowledge Analysis [in Russian]. IM SBRAS, Novosibirsk.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-af4940dd-6bc0-4783-9cf0-b2ab7fbced3f
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