Gower, John
(2003).
*metodološki zvezki (Develpments in Applied Statistics)*, 19 pp. 3–22.

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: | Journal Article |
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Copyright Holders: | 2003 Faculty of Social Sciences, University of Ljubljana, Slovenia |

ISSN: | 1854-0031 |

Academic Unit/Department: | Mathematics, Computing and Technology > Mathematics and Statistics |

Item ID: | 22648 |

Depositing User: | Sarah Frain |

Date Deposited: | 26 Aug 2010 12:50 |

Last Modified: | 02 Dec 2010 21:02 |

URI: | http://oro.open.ac.uk/id/eprint/22648 |

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