Pattern Recognition and Image Analysis

, Volume 28, Issue 4, pp 695–702 | Cite as

Structure Choice for Relations between Objects in Metric Classification Algorithms

  • N. A. IgnatyevEmail author
Mathematical Method in Pattern Recognition


We analyze the cluster structure of learning samples, decomposing class objects into disjoint groups. Decomposition results are used for the computation of the compactness measure for the sample and its minimal coverage by standard objects. We show that the number of standard objects depends on the metric choice, the distance to noise objects, the scales of the feature measurements, and nonlinear transformations of the feature space. We experimentally prove that the set of standards of the minimal coverage and noise objects affect the algorithm generalizing ability.


compactness measures spans of classes noise objects nonlinear transformations 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    N. G. Zagoruiko, O. A. Kutnenko, A. O. Zyryanov, and D. A. Levanov, “Learning to recognition without overfitting Обучение распознаванию образов без пере–обучения,” Mash. Obuch. Anal. Dannykh (Mach. Learn. Data Anal.) 1 (7), 891–901 (2014) [in Russian].Google Scholar
  2. 2.
    K. V. Vorontsov, “A combinatorial approach to estimating the quality of learning algorithms,” in Mathematical Problems in Cybernetics (Fizmatlit, Moscow, 2004), No. 13, pp. 5–36 [in Russian].Google Scholar
  3. 3.
    V. N. Vapnik, Reconstruction of functions from empirical data (Nauka, Moscow, 1979) [in Russian]; English transl.: Estimation of dependences based on empirical data (Springer–Verlag, New York–Berlin,1982).zbMATHGoogle Scholar
  4. 4.
    N. A. Ignat’ev, “Cluster analysis and choice of standard objects in supervised pattern recognition problems,” Vychisl. Tekhnol. 20 (6), 34–43 (2015).zbMATHGoogle Scholar
  5. 5.
    D. Y. Saidov, “Data visualization and its proof by compactness criterion of objects of classes,” Int. J. Intell. Syst. Appl. (IJISA) 9 (8), 51–58 (2017).Google Scholar
  6. 6. Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Uzbekistan National UniversityTashkentUzbekistan

Personalised recommendations