An efficient optimization method for revealing local optima of projection pursuit indices

Abstract

In order to summarize and represent graphically multidimensional data in statistics, projection pursuit methods look for projection axes which reveal structures, such as possible groups or outliers, by optimizing a function called projection index. To determine these possible interesting structures, it is necessary to choose an optimization method capable to find not only the global optimum of the projection index but also the local optima susceptible to reveal these structures. For this purpose, we suggest a metaheuristic which does not ask for many parameters to settle and which provokes premature convergence to local optima. This method called Tribes is a hybrid Particle Swarm Optimization method (PSO) based on a stochastic optimization technique developed in [2]. The computation is fast even for big volumes of data so that the use of the method in the field of projection pursuit fulfills the statistician expectations. © 2010 Springer-Verlag Berlin Heidelberg.