Exploratory Projection Pursuit

TLDR: A new projection pursuit algorithm for exploring multivariate data is presented that has both statistical and computational advantages over previous methods and the emphasis here is on the discovery of nonlinear effects such as clustering or other general nonlinear associations among the variables.

Abstract: A new projection pursuit algorithm for exploring multivariate data is presented that has both statistical and computational advantages over previous methods. A number of practical issues concerning its application are addressed. A connection to multivariate density estimation is established, and its properties are investigated through simulation studies and application to real data. The goal of exploratory projection pursuit is to use the data to find low- (one-, two-, or three-) dimensional projections that provide the most revealing views of the full-dimensional data. With these views the human gift for pattern recognition can be applied to help discover effects that may not have been anticipated in advance. Since linear effects are directly captured by the covariance structure of the variable pairs (which are straightforward to estimate) the emphasis here is on the discovery of nonlinear effects such as clustering or other general nonlinear associations among the variables. Although arbitrary ...