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Volume 29, No 1, 2022, P. 18-32 UDC 519.87+519.854
Keywords: NP-hardness, taxonomy (clustering), typical object (prototypes) selection, function of rival similarity. DOI: 10.33048/daio.2022.29.713 Olga A. Kutnenko 1,2 Received April 26, 2021 References[1] N. G. Zagoruiko, I. A. Borisova, V. V. Dyubanov, and O. A. Kutnenko, Methods of recognition based on the function of rival similarity, Pattern Recognit. Image Anal. 18 (1), 1–6 (2008).[2] I. A. Borisova, V. V. Dyubanov, N. G. Zagoruiko, and O. A. Kutnenko, Similarity and compactness, in Proc. 14th All-Russian Conf. “Mathematical Methods for Pattern Recognition”, Suzdal, Russia, Sept. 21–25, 2009 (Maks Press, Moscow, 2009), pp. 89–92 [Russian]. [3] C. J. C. Burges, A tutorial on support vector machines for pattern recognition, Data Mining Knowl. Discov. 2 (2), 121–167 (1998). [4] M. E. Tipping, The relevance vector machine, in Advances in Neural Information Processing Systems 12 (Proc. 1999 Conf., Denver, CO, USA, Nov. 29–Dec. 4, 1999) (MIT Press, Cambridge, MA, 2000), pp. 652–658. [5] N. G. Zagoruiko, Applied Methods of Data and Knowledge Analysis (Izd. Inst. Mat., Novosibirsk, 1999) [Russian]. [6] K. V. Vorontsov and A. O. Koloskov, Compactness profiles and prototype object selection in metric classification algorithms, Iskusstv. Intell., No. 2, 30–33 (2006) [Russian]. [7] M. N. Ivanov and K. V. Vorontsov, Prototypes selection based on minimization of a complete follow-control functional, in Proc. 14th All-Russian Conf. “Mathematical Methods for Pattern Recognition”, Suzdal, Russia, Sept. 21–25, 2009 (Maks Press, Moscow, 2009), pp. 119-–122 [Russian]. [8] S. Bermejo and J. Cabestany, Learning with nearest neighbor classifiers, Neural Proc. Lett. 13 (2), 159-–181 (2001). [9] V. N. Vapnik, The Task of Learning Pattern Recognition (Znanie, Moscow, 1971) [Russian]. [10] N. G. Zagoruiko, I. A. Borisova, V. V. Dyubanov, and O. A. Kutnenko, A quantitative measure of compactness and similarity in a competitive space, Sib. J. Ind. Math. 13 (1), 59–71 (2010) [Russian] [J. Appl. Ind. Math. 5 (1), 144–154 (2011)]. [11] I. A. Borisova, A taxonomy algorithm FRiS-Tax, Nauchn. Vestn. NGTU, No. 3, 3–12 (2007) [Russian]. [12] I. A. Borisova and N. G. Zagoruiko, A FRiS-TDR algorithm for solving a generalized taxonomy and recognition problem, in Proc. 2nd All-Russian Conf. “Knowledge–Ontology–Theory”, Novosibirsk, Russia, Oct. 22–24, 2009, Vol. 1 (Inst. Mat., Novosibirsk, 2009), pp. 93–102 [Russian]. [13] J. B. MacQueen, Some methods for classification and analysis of multivariate observations, in Proc. 5th Berkley Symp. Math. Stat. Prob., Berkley, USA, June 21–July 18, 1965; Dec. 27, 1965–Jan. 7, 1966, Vol. 1 (Univ. California Press, Berkley, 1967), pp. 281—297. [14] A. V. Zukhba, NP-completeness of the problem of prototype selection in the nearest neighbor method, Pattern Recognit. Image Anal. 20 (4), 484–494 (2010). [15] I. A. Borisova, V. V. Dyubanov, O. A. Kutnenko, and N. G. Zagoruiko, Use of the FRiS-function for taxonomy, attribute selection and decision rule construction, in Knowledge Processing and Data Analysis (Rev. Sel. Pap. 1st Int. Conf. KONT 2007, Novosibirsk, Russia, Sept. 14–16, 2007; 1st Int. Conf. KPP 2007, Darmstadt, Germany, Sept. 28–30, 2007) (Springer, Heidelberg, 2011), pp. 256–270 (Lect. Notes Comput. Sci., Vol. 6581). [16] N. G. Zagoruiko, I. A. Borisova, O. A. Kutnenko, and V. V. Dyubanov, A construction of a compressed description of data using a function of rival similarity, Sib. J. Ind. Math. 16 (1), 29–41 (2013) [Russian] [J. Appl. Ind. Math. 7 (2), 275–286 (2013)]. [17] I. A. Borisova, Computational complexity of the problem of choosing typical representatives in a 2-clustering of a finite set of points in a metric space, Discrete Anal. Oper. Res. 27 (2), 5–16 (2020) [Russian] [J. Appl. Ind. Math. 14 (2), 242–248 (2020)]. [18] M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, San Francisco, 1979; Mir, Moscow, 1982 [Russian]). |
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