Gower, John
(2003).
| URL: | http://mrvar.fdv.uni-lj.si/pub/mz/mz19/gower.pdf |
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| Google Scholar: | Look up in Google Scholar |
Abstract
The fundamental geometry is outlined that underlies all biplots of a data-matrix X of n cases and p variables. Cases are represented by n points and variables by a reference system. The reference system for quantitative variables may be orthogonal Cartesian axes, other linear axes or nonlinear trajectories. The reference system for categorical variables is a set of category-level-points (CLPs) one for each category-level; CLPs for ordered categories are collinear. Axes are labelled by a set of graduated numerical markers; CLPs are labelled by the names of their category levels. The point representing a case is nearer the markers that give the values of its variables, than to any other markers. This high dimensional representation is approximated in few (often two) dimensions in such a way that the approximated reference system gives optimal approximations to the values of X. Furthermore, new cases may be interpolated into the approximation space. Special cases within this general framework are illustrated by several examples of biplots.
| Item Type: | Article |
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| Copyright Holders: | 2003 Faculty of Social Sciences, University of Ljubljana, Slovenia |
| ISSN: | 1854-0031 |
| Academic Unit/School: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |
| Item ID: | 22648 |
| Depositing User: | Sarah Frain |
| Date Deposited: | 26 Aug 2010 12:50 |
| Last Modified: | 04 Oct 2016 10:42 |
| URI: | http://oro.open.ac.uk/id/eprint/22648 |
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