Clustering of Data Represented by Pairwise Comparisons

Aivazyan, S. A. et al. (1989) Applied Statistics. Classification and Reduction of Dimensionality [in Russian]. FiS, Moscow.Search in Google Scholar

Aizerman, M. A., Braverman, E. M. and Rozonoer, L. I. (1970) The Method of Potential Functions in Machine Learning Theory [in Russian]. Nauka, Moscow.Search in Google Scholar

Bognar, J. (1974) Indefinite Inner Product Spaces. Springer-Verlag, New York.Search in Google Scholar

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.Search in Google Scholar

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.Search in Google Scholar

Braverman, E. M. and Muchnik, I. B. (1983) Structured Methods of Empirical Data Processing [in Russian]. Nauka, Moscow.Search in Google Scholar

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).Search in Google Scholar

Duda, R. O. and Hart, P. E. (1973) Pattern Classification and Scene Analysis. Wiley, New York.Search in Google Scholar

Duda, R. O., Hart, P. E. and Stork, D. G. (2000) Pattern Classification.Wiley, New York.Search in Google Scholar

Dvoenko, S. D. (2001) Restoration of spaces in data by the method of non-hierarchical decompositions. Automation and Remote Control. 62, 467– 473. //doi.org/10.1023/A:1002814429456Search in Google Scholar

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.Search in Google Scholar

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.Search in Google Scholar

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.Search in Google Scholar

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.Search in Google Scholar

Dvoenko, S. and Owsinski, J. (2019) The permutable k-means for the bipartial criterion. Informatica. 43 (2), 253–262. //doi.org/10.31449/inf.v 43i2.2090Search in Google Scholar

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/S1054661818040089Search in Google Scholar

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/S1054661821020061Search in Google Scholar

Fisher, R. A. (1936) The use of multiple measurements in taxonomic problems. Ann. Eugenics. 7 (2), 179-188.Search in Google Scholar

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/10.1080/01621459.1967.10500923Search in Google Scholar

Harman, H. H. (1976) Modern Factor Analysis. University of Chicago Press, Chicago.Search in Google Scholar

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/10.2307/2346830Search in Google Scholar

Kemeny, J. (1959) Mathematics without numbers. Daedalus, 88(4), 577–591.Search in Google Scholar

Litvak, B. G. (1982) Expert Information: Methods of Acquisition and Analysis [in Russian]. Radio i Svyaz, Moscow.Search in Google Scholar

Lumel’sky, V. Ya. (1970) Grouping of parameters on the basis of communication matrices [in Russian]. Avtomat. i Telemekh. 1, 133–143.Search in Google Scholar

Luce, R. D. (1959) Individual Choice Behavior: A Theoretical Analysis. Wiley, New York.Search in Google Scholar

Mercer, J. (1909) Functions of positive and negative type and their connection with the theory of integral equations. Philos. Trans. Roy. Soc., London.Search in Google Scholar

Owsiński, J. W. (2020) Data Analysis in Bi-partial Perspective: Clustering and Beyond. SCI 818, Springer. //doi.org/10.1007/978-3-030-13389-4Search in Google Scholar

Pekalska, E. AND Duin R. P. W. (2005) The Dissimilarity Representation for Pattern Recognition. Foundations and Applications. World Scientific, Sngapore.Search in Google Scholar

Rosenblatt, F. (1962) Principles of Neurodynamics: Perceptrons and the Theory of Brain Mechanisms. Spartan Books, Washington.Search in Google Scholar

Schlesinger, M. (1965) About spontaneous recognition of patterns [in Russian]. Reading Automations. Kiev, 38–45.Search in Google Scholar

Späth, H. (1983) Cluster-Formation und -Analyse: Theorie, FORTRAN-Programme und Beispiele [in German]. R. Oldenbourg Verlag, München– Wien.Search in Google Scholar

Torgerson, W. S. (1958) Theory and Methods of Scaling. Wiley, New York.Search in Google Scholar

Ward, J. (1963) Hierarchical grouping to optimize an objective function. J. American Statist. Ass. 58 (301), 236–244. //doi.org/10.1080/01621459.1963.10500845Search in Google Scholar

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/BF02287916Search in Google Scholar

Zagoruiko, N. G. (1999) Applied Methods of Data and Knowledge Analysis [in Russian]. IM SBRAS, Novosibirsk.Search in Google Scholar