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Unfolding a symmetric matrix

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

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1007/BF01202583
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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 Ri and ri, so that a theoretical distance between the i-th and j-th samples is represented twice, once by the distance between Ri and rj and once by the distance between Rj and ri. Selfdistances between Ri andri 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
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
Item ID: 24130
Depositing User: Sarah Frain
Date Deposited: 11 May 2011 09:44
Last Modified: 11 May 2011 09:44
URI: http://oro.open.ac.uk/id/eprint/24130
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