Projection Pursuit Clustering for Exploratory Data Analysis

Abstract

Exploratory projection pursuit is a set of data analytic techniques for finding “interesting” low-dimensional projections of multivariate data. One particular interesting structure is that of clusters in the data. Projection pursuit clustering is a synthesis of projection pursuit and nonhierarchical clustering methods that simultaneously attempts to cluster the data and to find a low-dimensional representation of this cluster structure. We introduce a projection pursuit clustering index based on orthogonal canonical variates that takes account of scale in the data, and compare our index with one previously suggested. We show that the two indexes are identical when the data are sphered, and discuss when such sphering should be done. We also propose diagnostics for finding the optimum number of groups in projection pursuit clustering, and extend the technique to search for clusters in higher dimensions. All the methodology is illustrated and evaluated on one simulated and two real datasets.