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A Density Distance Based Approach to Projection Pursuit Discriminant Analysis

  • Laura Lizzani
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

In this paper a brief review of the main contributions to projection pursuit discriminant analysis is presented. A new procedure, based on distance measures between probability densities, is developed in order to obtain linear discriminant functions, which best separate different populations. In the two- group case, Matusita’s distance between the projected population density functions is adopted as projection index; while, in the multi-group case, a monotone transformation of Matusita’s affinity coefficient is employed to measure the separation among the marginal probability density functions of the different populations. Simulation studies stress the efficacy of the proposed method in comparison with classical parametric ones and with the projection pursuit based linear discriminant procedure developed by Posse.

Key words

Matusita’s Affinity Coefficient Projection Pursuit Discriminant Analysis Matusita’s Distance Coefficient 

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References

  1. Bhattacharyya, A. (1943). On a measure of divergence between two statistical populations defined by their probability distributions, Bulletin of the Calcutta Mathematical Society, 35, 99–109.Google Scholar
  2. Calò, D. & Montanari, A. (1997). An empirical discrimination algorithm based on projection pursuit density estimation, Book of Short Papers, Classification and Data Analysis, Meeting of the Classification Group of Società Italiana di Statistica, Pescara, 3-4 luglio, 65–68.Google Scholar
  3. Chen, Z. & Muirhead, R.J. (1994). A comparison of robust linear discriminant procedures using projection pursuit methods, in Multivariate Analysis and its Applications, IMS Lecture Notes-Monograph Series, Hayward, 24, 163–176.Google Scholar
  4. Flick, T.E. & Jones, L.K. & Priest, R.G. & Herman, N.C. (1990). Pattern classification using projection pursuit, Pattern Recognition, 12, 1367–1376.CrossRefGoogle Scholar
  5. Friedman, J.H. (1985). Classification and multiple regression through projection pursuit, Technical Report 12, Laboratory for Computational Statistics, Department of Statistics, Stanford University.Google Scholar
  6. Friedman, J.H. & Tukey, J. (1974). A projection pursuit algorithm for exploratory data analysis, IEEE Transactions on Computers, 23, 881–889.CrossRefGoogle Scholar
  7. Glick, N. (1973). Separation and probability of correct classification among two or more distributions, Annals of the Institute of Statistical Mathematics, 25, 373–382.CrossRefGoogle Scholar
  8. Henry, D.H. (1983). Multiplicative models in projection pursuit, Ph. D. Thesis, Stanford Linear Accelerator Center, Stanford University.Google Scholar
  9. Huber, P.J. (1985). Projection pursuit, The Annals of Statistics, 13, 435–475.CrossRefGoogle Scholar
  10. Huber, P.J. (1990). Algorithms for projection pursuit, Technical Report 3, Department of Mathematics, M.I.T. Cambridge.Google Scholar
  11. Krzanowski, W.J. (1988). Principles of multivariate analysis, Oxford Science Publication, New York, 359–360.Google Scholar
  12. Matusita, K. (1956). Decision rule, based on distance, for the classification problem, Annals of the Institute of Statistical Mathematics, 8, 67–77.CrossRefGoogle Scholar
  13. Matusita, K. (1967). On the notion of affinity of several distributions and some of its applications, Annals of the Institute of Statistical Mathematics, 19, 181–192.CrossRefGoogle Scholar
  14. Montanari, A. & Lizzani, L. (1996). Projection pursuit e scelta delle variabili, Atti della XXXVIII Riunione Scientifica della Società Italiana di Statistica, 2, 591–598.Google Scholar
  15. Polzehl, J. (1995). Projection pursuit discriminant analysis, Computational Statistics and Data Analysis, 20, 141–157.CrossRefGoogle Scholar
  16. Posse, C. (1992). Projection pursuit discriminant analysis for two groups, Communications in Statistics - Theory and Methods, 21, 1–19.CrossRefGoogle Scholar
  17. Roosen, C.B. & Hastie, T.J. (1993). Logistic response projection pursuit regression, Statistics and Data Analysis Research Department, AT&T Bell Laboratories, Doc. BL011214-930806-09TM.Google Scholar
  18. Sheather, S.J. & Jones, M.C. (1991). A reliable data-based bandwidth selection method for kernel density estimation, Journal of the Royal Statistical Society, Series B, 93, 683–690.Google Scholar
  19. Silverman, B.W. (1986). Density estimation for statistics and data analysis, Chapman and Hall, London.Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1998

Authors and Affiliations

  • Laura Lizzani
    • 1
  1. 1.Dipartimento di Scienze StatisticheUniversità di BolognaBolognaItalia

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