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On the forward and backward algorithms of projection pursuit. (English) Zbl 1105.62334
Summary: This article provides a historic review of the forward and backward projection pursuit algorithms, previously thought to be equivalent, and points out an important difference between the two. In doing so, a small error in the original exploratory projection pursuit article by J.H. Friedman [J. Am. Stat. Assoc. 82, 249–266 (1987; Zbl 0664.62060)] is corrected. The implication of the difference is briefly discussed in the context of an application in which projection pursuit density estimation is used as a building block for nonparametric discriminant analysis.

MSC:
62G07 Density estimation
62H30 Classification and discrimination; cluster analysis (statistical aspects)
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References:
[1] Friedberg, S. H., Insel, A. J. and Spence, L. E. (1989). Linear Algebra , 2nd ed. Prentice-Hall, Englewood Cliffs, NJ. · Zbl 0695.15001
[2] Friedman, J. H. (1987). Exploratory projection pursuit. J. Amer. Statist. Assoc. 82 249–266. · Zbl 0664.62060
[3] Friedman, J. H., Stuetzle, W. and Schroeder, A. (1984). Projection pursuit density estimation. J. Amer. Statist. Assoc. 79 599–608.
[4] Huber, P. J. (1985). Projection pursuit (with discussion). Ann. Statist. 13 435–525. JSTOR: · Zbl 0595.62059
[5] Polzehl, J. (1995). Projection pursuit discriminant analysis. Comput. Statist. Data Anal. 20 141–157. · Zbl 0875.62272
[6] Zhu, M. and Hastie, T. J. (2003). Feature extraction for nonparametric discriminant analysis. J. Comput. Graph. Statist. 12 101–120.
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