Gower, John C. and Greenacre, Michael J.
(1996).
*Journal of Classification*, 13(1) pp. 81–105.

DOI (Digital Object Identifier) Link: | http://doi.org/10.1007/BF01202583 |
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Google Scholar: | Look up in Google Scholar |

## Abstract

Graphical displays which show inter-sample distances are important for the interpretation and presentation of multivariate data. Except when the displays are two-dimensional, however, they are often difficult to visualize as a whole. A device, based on multidimensional unfolding, is described for presenting some intrinsically high-dimensional displays in fewer, usually two, dimensions. This goal is achieved by representing each sample by a pair of points, say *R*_{i} and *r*_{i}, so that a theoretical distance between the *i*-th and *j*-th samples is represented twice, once by the distance between *R*_{i} and *r*_{j} and once by the distance between *R*_{j} and *r*_{i}. Selfdistances between *R*_{i} and*r*_{i} need not be zero. The mathematical conditions for unfolding to exhibit symmetry are established. Algorithms for finding approximate fits, not constrained to be symmetric, are discussed and some examples are given.

Item Type: | Journal Article |
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Copyright Holders: | 1996 Springer |

ISSN: | 1432-1343 |

Keywords: | dimensionality reduction; distances; graphics; multidimensional scaling; symmetric matrices; unfolding |

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

Item ID: | 24130 |

Depositing User: | Sarah Frain |

Date Deposited: | 11 May 2011 09:44 |

Last Modified: | 15 Jan 2016 15:04 |

URI: | http://oro.open.ac.uk/id/eprint/24130 |

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