A Characterization of Principal Components for Projection Pursuit

Principal component analysis is a technique often found to be useful for identifying structure in multivariate data. Although it has various characterizations (Rao 1964), the most familiar is as a variance-maximizing projection. Projection pursuit is a methodology for selecting low-dimensional projections of multivariate data by the optimization of some index of "interestingness" 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 likelihood under the assumption of normality.