Projection Pursuit via White Noise Matrices

• Activity Number: 209
• Type: Invited
• Date/Time: Monday, August 1, 2011 : 2:00 PM to 3:50 PM
• Sponsor: International Indian Statistical Association
• Author(s): Bruce George Lindsay*+
• Companies: Penn State University
• Keywords: projection pursuit ; white noise ; exploratory data analysis ; dimension reduction

Abstract

Projection pursuit dates back to 1974 (Friedman and Tukey). The goal is to find the most interesting projections of high dimensional data, where interesting is often defined to mean non-normal. The word "pursuit" arises from the numerical challenge of finding best projections. In this paper, the most interesting projection is the one that has the least conditional normality. This definition is turned into a statistical method by the construction of a white noise matrix based on the Fisher information matrix, and using the result that the normal distribution satisfies a minimal information property. An eigen-analysis of the white noise matrix yields both the most interesting and least interesting projections as the eigenvectors corresponding to the largest and smallest eigenvalues. The matrix is called a white noise matrix because if a projection is "white noise", in the sense of being marginally normal and independent of all orthogonal projections, it is an eigenvector with zero eigenvalue. A computationally fast, and statistically robust, estimator of the information matrix is developed, and used to find interesting directions in historically important and new data sets.