Re‐centered kurtosis as a projection pursuit index for multivariate data analysis

Abstract

High‐dimensional data, which have become common in analytical chemistry, are often rich in information, but useful information may not be discovered without applying advanced data analysis methods. As a powerful tool for exploratory data analysis, projection pursuit (PP) is less widely used in chemistry compared with other methods such as principal component analysis (PCA), although PP often gives better results than PCA. PP does not have a uniquely defined objective function (projection index), and different statistics have been proposed as projection indices. Kurtosis has been widely employed as a projection index, and minimization of kurtosis is helpful in revealing clusters. However, this method often fails when the clusters in a data set are not balanced (i.e., present in unequal proportions). In this work, a newly defined kurtosis, referred to as “re‐centered kurtosis,” is proposed as a projection index. The theory and the optimization algorithms for the re‐centered kurtosis are developed. The utility of the PP method using the proposed re‐centered kurtosis as a projection index to reveal unbalanced clusters is demonstrated by simulated and real experimental data. Copyright © 2013 John Wiley & Sons, Ltd.