Exploratory Projection Pursuit

Abstract

Exploratoryprojection pursuit is concerned with finding relatively highly revealing lower dimensional projections of high dimensional data. The intent is to discover views of the multivariate data set that exhibit nonlinear effectsclustering, concentrations near nonlinear manifolds -that are not captured by the linear correlation structure. This paper presents a new algorithm for this purpose that has both statistical and computational advantages over previous methods.A connection to density estimation is established. Examples are presented and issues related to practical application are discussed.

A Projection Pursuit framework for supervised dimension reduction of high dimensional small sample datasets

“…Once a 1 is found, SPP tries to remove all the information captured in that direction from the original data in order to avoid finding the same projection direction in subsequent iterations. For this task, the original SPP uses a "structure removal" procedure [14], which "Gaussianize" the data in the found direction, as follows:…”

“…Early approaches in this respect were based on the gradient techniques [30,29] and Newton-Raphson [31,37,14,13], where the projections are performed in at most three dimensions for visual exploratory tasks, the so-called exploratory projection pursuit (EPP). Further developments focused on developing more global methods for PP optimization, such as random search [38,39,29], genetic algorithm (GA) [32], random scan sampling algorithm (RSSA) [34], simulated annealing (SA) [21], particle swarm optimization (PSO) [35] and tribes [40].…”

“…Projection pursuit (PP) [13,14] is a FE method that has been successfully applied in several domains for both supervised and unsupervised analyses (e.g. [15][16][17][18]).…”

“…Evidently, the problem worsens as p or m increase. Traditional PP optimizers based on the gradients or Newton methods [29][30][31]19] are usually inadequate for such a kind of data due to the vastness of possible projections and, thus, the high susceptibility to find poor local optima [14]. More global PP optimizers were described recently, including genetic algorithms (GA) [32,33], simulating annealing (SA) [21], random scan sampling (RSSA) [34] and particle swarm optimization (PSO) [35].…”

Fast Projection Pursuit Based on Quality of Projected Clusters

“…Projection pursuit (PP) searches for the most "interesting" projections of multidimensional data by optimizing some objective functions referred to as the projection index [1,2]. Many projection indices have been introduced, both for unsupervised and for supervised learning.…”