A characterization of principal components for projection pursuit

Principal component analysis is a technique often found to be useful for id entifying structure in multivariate data. Although it has various character izations (Rao 1964), the most familiar is as a variance-maximizing projecti on. Projection pursuit is a methodology for selecting low-dimensional proje ctions of multivariate data by the optimization of some index of "interesti ngness" over all projection directions. Principal component analysis can be viewed as an example of projection pursuit, and we justify its success in structure identification by characterizing it in terms of maximum likelihoo d under the assumption of normality.