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Clustering of data represented by pairwise comparisons

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, experimental data, given in the form of pairwise comparisons, such as distances or similarities, are considered. Clustering algorithms for processing such data are developed based on the well-known k-means procedure. Relations to factor analysis are shown. The problems of improving clustering quality and of finding the proper number of clusters in the case of pairwise comparisons are considered. Illustrative examples are provided.
Słowa kluczowe
Rocznik
Strony
343--387
Opis fizyczny
Bibliogr. 35 poz., rys., tab.
Twórcy
  • Tula State University, Tula, Russia
Bibliografia
  • Aivazyan, S. A. et al. (1989) Applied Statistics. Classification and Reduction of Dimensionality [in Russian]. FiS, Moscow.
  • Aizerman, M. A., Braverman, E. M. and Rozonoer, L. I. (1970) The Method of Potential Functions in Machine Learning Theory [in Russian]. Nauka, Moscow.
  • Bognar, J. (1974) Indefinite Inner Product Spaces. Springer-Verlag, New York.
  • Braverman, E. M. (1970) Methods of extremal grouping of parameters and problem of apportionment of essential factors [in Russian]. Avtomat. i Telemekh. 1, 123–132.
  • Braverman, E. M. et al. (1971) Diagonalization of the relation matrix and detecting hidden factors [in Russian]. Trans. Inst. of Control Sciences. 1 st Issue “Problems of increasing of automata possibilities.” ICS, Moscow, 42–79.
  • Braverman, E. M. and Muchnik, I. B. (1983) Structured Methods of Empirical Data Processing [in Russian]. Nauka, Moscow.
  • Diday, E., Bochi, S., Brossier, G. and Celeux, G. (1979) Optimisation en Classification Automatique. 2. Institut national de recherche en informatique et en automatique (INRIA), Le Chesnay (in French).
  • Duda, R. O. and Hart, P. E. (1973) Pattern Classification and Scene Analysis. Wiley, New York.
  • Duda, R. O., Hart, P. E. and Stork, D. G. (2000) Pattern Classification. Wiley, New York.
  • Dvoenko, S. D. (2001) Restoration of spaces in data by the method of nonhierarchical decompositions. Automation and Remote Control. 62, 467–473. //doi.org/10.1023/A:1002814429456
  • Dvoenko, S. D. (2009a) 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. (2009b) Clustering of a set described by paired distances and closeness between its elements [in Russian]. Sib. J. of Industr. Math. 12(1), 61–73.
  • Dvoenko, S. D. (2011) On clustering of a set of members by distances and similarities. Proc. of 11th Int. Conf. on Pattern Recognition and Information Processing (PRIP’2011). BSUIR, 104–107.
  • Dvoenko, S. (2014) Meanless k-means as k-meanless clustering with the bipartial approach. Proc. of 12th Int. Conf. on Pattern Recognition and Information Processing (PRIP’2014). UIIP NASB, 50–54.
  • Dvoenko, S. and Owsinski, J. (2019) The permutable k-means for the bipartial criterion. Informatica. 43(2), 253–262. //doi.org/10.31449/inf.v43i2.2090
  • 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. //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. //doi.org/10.1134/S1054661821020061
  • Fisher, R. A. (1936) The use of multiple measurements in taxonomic problems. Ann. Eugenics. 7(2), 179-188.
  • Friedman, H. P. and Rubin, J. (1967) On some invariant criteria for grouping data. Journal of the American Statistical Association 62 (320), 1159–1178. //doi.org/10.1080/01621459.1967.10500923
  • Harman, H. H. (1976) Modern Factor Analysis. University of Chicago Press, Chicago.
  • Hartigan, J. A. and Wong, M. A. (1979) Algorithm AS 136: A k-means clustering algorithm. J. Roy. Soc. 28(1), 100–108. //doi.org/10.2307/2346830
  • Kemeny, J. (1959) Mathematics without numbers. Daedalus, 88(4), 577–591.
  • Litvak, B. G. (1982) Expert Information: Methods of Acquisition and Analysis [in Russian]. Radio i Svyaz, Moscow.
  • Lumel’sky, V. Ya. (1970) Grouping of parameters on the basis of communication matrices [in Russian]. Avtomat. i Telemekh. 1, 133–143.
  • Luce, R. D. (1959) Individual Choice Behavior: A Theoretical Analysis. Wiley, New York.
  • Mercer, J. (1909) Functions of positive and negative type and their connection with the theory of integral equations. Philos. Trans. Roy. Soc., London.
  • Owsiński, J. W. (2020) Data Analysis in Bi-partial Perspective: Clustering and Beyond. SCI 818, Springer. //doi.org/10.1007/978-3-030-13389-4
  • Pekalska, E. and Duin R. P. W. (2005) The Dissimilarity Representation for Pattern Recognition. Foundations and Applications. World Scientific, Sngapore.
  • Rosenblatt, F. (1962) Principles of Neurodynamics: Perceptrons and the Theory of Brain Mechanisms. Spartan Books, Washington.
  • Schlesinger, M. (1965) About spontaneous recognition of patterns [in Russian]. Reading Automations. Kiev, 38–45.
  • Späth, H. (1983) Cluster-Formation und -Analyse: Theorie, FORTRAN-Programme und Beispiele [in German]. R. Oldenbourg Verlag, München–Wien.
  • Torgerson, W. S. (1958) Theory and Methods of Scaling. Wiley, New York.
  • Ward, J. (1963) Hierarchical grouping to optimize an objective function. J. American Statist. Ass. 58(301), 236–244. //doi.org/10.1080/01621459.1963.10500845
  • Young, G. and Householder, A. S. (1938) Discussion of set of points in terms of their mutual distances. Psychometrica. 3, 19–22. //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-8b250b28-4ccc-4c37-8bc5-3ad68a8531ba
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