On the Forward and Backward Algorithms of Projection Pursuit1 by Mu Zhu

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 Friedman [J. Amer. Statist. Assoc. 82 (1987) 249–266] 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.