Projection pursuit in high dimensions

Projection pursuit is a multivariate statistical technique aimed at finding interesting data projections. It suffers from several problems when applied to high-dimensional datasets. These problems are investigated within the framework of skewness-based projection pursuit, when the interesting projections are the maximally skewed ones. We address the problems by means of generalized tensor eigenvectors and symmetrizing linear projections. We illustrate the problems and the proposed solutions with a simple dataset with more variables than units.