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.
"On the forward and backward algorithms of projection pursuit." Ann. Statist. 32 (1) 233 - 244, February 2004. https://doi.org/10.1214/aos/1079120135