Genetic algorithms and particle swarm optimization for exploratory projection pursuit

Exploratory Projection Pursuit (EPP) methods have been developed thirty years ago in the context of exploratory analysis of large data sets. These methods consist in looking for low-dimensional projections that reveal some interesting structure existing in the data set but not visible in high dimension. Each projection is associated with a real valued index which optima correspond to valuable projections. Several EPP indices have been proposed in the statistics literature but the main problem lies in their optimization. In the present paper, we propose to apply Genetic Algorithms (GA) and recent Particle Swarm Optimization (PSO) algorithm to the optimization of several projection pursuit indices. We explain how the EPP methods can be implemented in order to become an efficient and powerful tool for the statistician. We illustrate our proposal on several simulated and real data sets.