Advertisement

Statistics and Computing

, Volume 17, Issue 1, pp 11–21 | Cite as

Optimal predictive partitioning

  • David J. Hand
  • Wojtek J. KrzanowskiEmail author
  • Martin J. Crowder
Article
  • 108 Downloads

Abstract

In many situations, one wishes to group objects into well-defined classes on the basis of one set of descriptor variables, and then predict the classes of new objects from a different set of variables. For example, a bank may categorise customers into distinct financial behaviour pattern classes by observing how they have behaved over a period of years, and then seek to assign new customers to future behaviour classes using information captured when they open an account. Such situations require the striking of a compromise between the compactness and integrity of the cluster structure, and the accuracy of the predictive assignment to clusters. We describe two algorithms for achieving such a compromise, discuss some of their features, and illustrate their performance in a simulation study and in a liver transplant problem.

Keywords

Alternating least squares Clustering Criterion optimisation Discrimination Error rates Transfer algorithm 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arabie P., Hubert, L.J., and DeSoete G. 1996. Clustering and Classification. Singapore, World Scientific.zbMATHGoogle Scholar
  2. Banfield C.F. and Bassill L.C. 1977. A transfer algorithm for non-hierarchical classification. Algorithm AS113: Applied Statistics 26: 206–210.CrossRefGoogle Scholar
  3. Benton T.C. and Hand D.J. 2002. Segmentation into predictable classes. IMA Journal of Management Mathematics 13: 245–259.zbMATHCrossRefMathSciNetGoogle Scholar
  4. Bock H.H. 1987. On the interface between cluster analysis, principal component analysis and multidimensional scaling. In: Bozdogan H. and Gupta A. K. (Eds.), Multivariate Statistical Modeling and Data Analysis. Dordrecht, Reidel, pp. 17–34.Google Scholar
  5. Bolton R.J. and Krzanowski W.J. 2003. Projection pursuit clustering for exploratory data analysis. Journal of Computational and Graphical Statistics 12: 121–142.CrossRefMathSciNetGoogle Scholar
  6. Everitt B.S., Landau S., and Leese M. 2001. Cluster Analysis (4th Ed). London, Arnold.Google Scholar
  7. Forgey E.W. 1965. Cluster analysis of multivariate data: efficiency versus interpretability of classification. Biometrics, 21: 768–769.Google Scholar
  8. Friedman J.H. and Meulman J.J. 2004. Clustering objects on subsets of attributes (with discussion). Journal of the Royal Statistical Society Series B 66: 815–849.Google Scholar
  9. Gordon A.D. 1999. Classification (2nd edn). Boca Raton, Chapman & Hall/CRC.zbMATHGoogle Scholar
  10. Gower J.C. 1974. Maximal predictive classification. Biometrics, 30: 643–654.zbMATHCrossRefGoogle Scholar
  11. Hand D.J. 1997. Construction and Assessment of Classification Rules. Chichester, John Wiley & Sons.zbMATHGoogle Scholar
  12. Hand D.J., Li H.G., and Adams N.M. 2001. Supervised classification with structured class definitions. Computational Statistics and Data Analysis 36: 209–225.zbMATHCrossRefMathSciNetGoogle Scholar
  13. Hand D.J., Oliver J.J., and Lunn A.D. 1998. Discriminant analysis when the classes arise from a continuum. Pattern Recognition 31: 641–650.CrossRefGoogle Scholar
  14. Hartigan J.A. and Wong M.A. 1979. A k-means clustering algorithm. Algorithm AS136 Applied Statistics, 28: 100–108.zbMATHCrossRefGoogle Scholar
  15. Kelly M.G., Hand D.J., and Adams N.M. 1998. Defining the goals to optimise data mining performance. In: Agrawal R., Stolorz P., and Piatetsky-Shapiro G. (Eds.), Proceedings of the Fourth International Conference on Knowledge Discovery and Data Mining, Menlo Park, AAAI Press, pp. 234–238.Google Scholar
  16. Kelly M.G. and Hand D.J. 1999. Credit scoring with uncertain class definitions. IMA Journal of Mathematics Applied in Business and Industry, 10: 331–345.zbMATHGoogle Scholar
  17. Kelly M.G., Hand D.J., and Adams N.M. 1999. Supervised classification problems: how to be both judge and jury. In: Hand D.J., Kok J.N., and Berthold M.R. (Eds.), Advances in Intelligent Data Analysis Berlin, Springer, pp. 235–244.Google Scholar
  18. Krzanowski W.J. and Marriott F.H.C. 1995. Multivariate Analysis, part 2: Classification, Covariance Structures, and Repeated Measurements. London, Arnold.zbMATHGoogle Scholar
  19. Lewis E.M. 1994. An Introduction to Credit Scoring. San Rafael, California, Athena Press.Google Scholar
  20. MacQueen J. 1967. Some methods for classification and analysis of multivariate observations. In: LeCam L. and Neyman J., (Eds.), Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability. Berkeley, University of California Press, Vol. 1, pp. 281–297.Google Scholar
  21. McLachlan G.J. 1992. Discriminant Analysis and Statistical Pattern Recognition. New York, John Wiley & Sons.CrossRefGoogle Scholar
  22. Ward, J.H. 1963. Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association 58: 236–244.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • David J. Hand
    • 1
    • 3
  • Wojtek J. Krzanowski
    • 2
    Email author
  • Martin J. Crowder
    • 1
  1. 1.Department of MathematicsImperial College of Science, Technology and MedicineLondonUK
  2. 2.School of Engineering, Computer Science and MathematicsUniversity of ExeterExeterUK
  3. 3.Institute for Mathematical SciencesImperial College of Science, Technology and MedicineLondonUK

Personalised recommendations