Three-Dimensional Projection Pursuit

The development and usage of a three-dimensional projection pursuit software package is discussed. The well-established Jones and Sibson moments index is chosen as a computationally efficient projection index to extend to 3D. Computer algebraic methods are extensively employed to handle the long and complex formulae that constitute the index and are explained in detail. A discussion of important practical issues such as interpreting projection solutions, dealing with outliers and optimization techniques completes the description of the development of the index. The article presents a tutorial introduction to freely available software that performs 3D projection pursuit. The tutorial uses the well-known Lubischew beetle data and an artificial tetrahedral data set to demonstrate how 3D projection pursuit can produce better clusters than those obtained by principal components analysis. The preferred method of using the software is via software functions from the computer package S. This not only provides the statistical user with a familiar interface but also permits the provision of full help and extensive graphics which contribute to a better understanding of the user’s data. The 3D index was initially developed to find interesting linear combinations of spectral bands in a multispectral image. The main example shows how 3D projection pursuit can successfully combine bands to discover alternative clusters to those produced by, say, principal components.