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An Algorithm with Projection Pursuit for Sliced Inverse Regression Model

  • Masahiro Mizuta
  • Hiroyuki Minami
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

In the paper, we investigate a conditional density function of sliced response variables and propose an algorithm for the sliced inverse regression (SIR) model with projection pursuit.

The SIR model is a general model for dimension reduction of explanatory variables on regression analysis. Some algorithms for SIR model are proposed; SIR, SIR2, Bivariate SIR. We apply the algorithms to some typical data sets. They can not find suitable reductions for all of the data sets. The proposed algorithm can get reasonable results for all of them.

Keywords

Explanatory Variable Projection Pursuit Slice Inverse Regression Suitable Reduction Ordinary Regression Analysis 
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.

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References

  1. FRIEDMAN, J. H. (1987): Exploratory Projection Pursuit, Journal of the American Statistical Association, 82, 249–266.CrossRefGoogle Scholar
  2. FRIEDMAN, J. H. & TUKEY, J. W. (1974): A Projection Pursuit Algorithm for Exploratory Data Analysis. IEEE Trans, on Computer, c-23, 9, 881–890.CrossRefGoogle Scholar
  3. KOYAMA, K., MORITA, A., MIZUTA, M., and SATO, Y. (1998): Projection Pursuit into Three Dimensional Space.(in Japanese) The Japanese Journal of Behaviormetrics, 25(1), 1–9.Google Scholar
  4. LEE, Y., LEE, D. and CHOI, K.(1998): Bivariate Sliced Inverse Regression and its Application. Data Science, Classification, and Related Methods, ISTAT, 198–201.Google Scholar
  5. LI, KER-CHAU (1991): Sliced Inverse Regression for Dimension Reduction. Journal of the American Statistical Association, 86, 316– 342.CrossRefGoogle Scholar
  6. MIZUTA, M. (1998): A New Algorithm for Sliced Inverse Regression with Projection Pursuit, (in Japanese) Proceedings of Japan Statistical Society 1998, 158–159.Google Scholar
  7. MIZUTA, M. (1999): Sliced Inverse Regression with Projection Pursuit., In: H. Bacelar-Nicolau, F. Costa Nicolau and J. Janssen (Eds.): Applied Stochastic Models and Data Analysis. INSTITUTO NACIONAL DE ESTATÍSTICA), 51–56.Google Scholar
  8. MIZUTA, M. (1999): Projection Pursuit into High Dimensional Space and its Applications. Bulletin of the International Statistical Institute, 52nd Session, 313–314Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 2000

Authors and Affiliations

  • Masahiro Mizuta
    • 1
  • Hiroyuki Minami
    • 1
  1. 1.Center for Information and Multimedia StudiesHokkaido UniversitySapporoJapan

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