Projection Pursuit Based on Gaussian Mixtures and Evolutionary Algorithms

Abstract

We propose a projection pursuit (PP) algorithm based on Gaussian mixture models (GMMs). The negentropy obtained from a multivariate density estimated by GMMs is adopted as the PP index to be maximized. For a fixed dimension of the projection subspace, the GMM-based density estimation is projected onto that subspace, where an approximation of the negentropy for Gaussian mixtures is computed. Then, genetic algorithms are used to find the optimal, orthogonal projection basis by maximizing the former approximation. We show that this semiparametric approach to PP is flexible and allows highly informative structures to be detected, by projecting multivariate datasets onto a subspace, where the data can be feasibly visualized. The performance of the proposed approach is shown on both artificial and real datasets. Supplementary materials for this article are available online.

Keywords:

• Clustering analysis
• Clustering visualization
• Data visualization
• Dimension-reduction method
• Multivariate data analysis

Acknowledgments

The authors are grateful to the editor, the associate editor, and two anonymous reviewers for their very helpful comments and suggestions which helped to improve the article.