Three-Dimensional Projection Pursuit (1995)
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| Venue: | J. Royal Statistical Society, Series C |
| Citations: | 9 - 0 self |
BibTeX
@ARTICLE{Nason95three-dimensionalprojection,
author = {Guy Nason},
title = {Three-Dimensional Projection Pursuit},
journal = {J. Royal Statistical Society, Series C},
year = {1995},
volume = {44},
pages = {411--430}
}
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Abstract
This article discusses various aspects of projection pursuit into three dimensions. The aim of projection pursuit is to find interesting linear combinations of variables in a multivariate data set. The precise definition of "interesting" is given later but clusters and other forms of non-linear structure are interesting. One- and twodimensional projection pursuit have been dealt with extensively in the literature and some excellent software implementations are available. The benefit of projection into three-dimensions is that more complex structures can be identified than with lower-dimensional projections. Projection pursuit into three dimensions is particularly attractive for two further perceptual reasons. Firstly, colours naturally correspond to 3-vectors, for example through the RGB representation. Secondly, point clouds and other objects in three dimensions can be investigated on computer screens. For example through spinning 3D plots, which are immediately comprehensible because of our 3D intuition. These reasons are important when applying 3D projection pursuit to multispectral images (colour) and multivariate data sets (intuition). Section 2 briefly describes projection pursuit and includes details on projection indices and the process of sphering. Section 3 explains that we have chosen to extend Jones and Sibson's (1987) well-known moments index into three dimensions because of its computational efficiency. The formulae for the moments index were analytically computed by the computer algebra package REDUCE (see Section 3.3). Section 3 also addresses the differentiation and optimization of the moments index, examines how outliers can be treated to provide better projection solutions and discusses how optimal projections can be rotated to give solutions that a...
