Mathematical Classification and Clustering: From How to What and Why

  • B. Mirkin
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


Although some clustering techniques are well known and widely used, their theoretical foundations are still unclear. We consider an approach, approximation clustering, as a unifying framework for making theoretical foundations to some popular techniques. The questions of interrelation of the models with each other and with some other methods (especially in contingency and spatial data analyses) are also discussed.


Cluster Technique Inal Variable Conceptual Cluster Spatial Data Analysis Approximation Cluster 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. BREIMAN, L., FRIEDMAN, J.H., OLSHEN, R.A., and STONE, C.J. (1984): Classification and Regression Trees. Wadswarth International Group, Belmont, Ca.Google Scholar
  2. BURT, P.J., and ADELSON, E.H. (1983): The Laplacian pyramid as a compact image code. IEEE Transactions on Communications V COM-31, 532–540.CrossRefGoogle Scholar
  3. FISHER, D.H. (1987): Knowledge acquisition via incremental conceptual clustering. Machine Learning, 2, 139–172.Google Scholar
  4. JAIN, A.K. and DUBES, R.C. (1988): Algorithms for Clustering Data. Prentice Hall, Englewood Cliffs, NJ.Google Scholar
  5. KAY, J. (1994): Wavelets. Advances in Applied Statistics, 2, 209–224.Google Scholar
  6. MALLAT, S.G. (1989): Multiresolution approximations and wavelet orthonormal bases on L 2 (R). Transactions of the American Mathematical Society, 315, 69–87.Google Scholar
  7. MIRKIN, B. (1996): Mathematical Classification and Clustering. Kluwer Academic Press, Dorderecht.CrossRefGoogle Scholar
  8. MIRKIN, B. (1997): Concept learning and feature selecting based on square-error clustering. Machine Learning (to appear).Google Scholar
  9. MIRKIN, B. (1998): Linear embedding of binary hierarchies and its applications. In: B. Mirkin, F. McMorris, F. Roberts and A. Rzhetsky (eds.): Mathematical Hierarchies and Biology. DIMACS AMS Series. American Mathematical Society, Providence (to appear).Google Scholar
  10. MIRKIN, B., ARABIE, P., and HUBERT, L. (1995): Additive two-mode cluster- ing: the error-variance approach revisited. Journal of Classification, 12, 243–263.CrossRefGoogle Scholar
  11. SAMET, H. (1990): The Design and Analysis of Spatial Data Structures. Addison-Wesley Series on Computer Science and Information Processing. Addison-Wesley Publishing Company, Amsterdam.Google Scholar
  12. WARD, J.H., Jr (1963): Hierarchical grouping to optimize an objective function, Journal of American Statist. Assoc., 58, 236–244.CrossRefGoogle Scholar
  13. WNEK, J. and MICHALSKI, R.S. (1994): Hypothesis-driven constructive induction in AQ17-HCI: A method and experiments, Machine Learning, 14, 139–168.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1998

Authors and Affiliations

  • B. Mirkin
    • 1
    • 2
  1. 1.DIMACSRutgers UniversityPiscatawayUSA
  2. 2.CEMIMoscowRussia

Personalised recommendations