Group average representations in Euclidean distance cones

Albers, Casper; Critchley, Frank and Gower, John (2007). Group average representations in Euclidean distance cones. In: Brito, Paula; Bertrand, Patrice; Cucumel, Gucumel and de Carvalho, Francisco eds. Selected Contributions in Data Analysis and Classification. Studies in Classification, Data Analysis, and Knowledge Organization. Berlin, Germany: Springer, pp. 445–454.

DOI (Digital Object Identifier) Link:	http://dx.doi.org/doi:10.1007/978-3-540-73560-1_41
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Abstract

The set of Euclidean distance matrices has a well-known representation as a convex cone. The problems of representing the group averages of K distance matrices are discussed, but not fully resolved, in the context of SMACOF, Generalized Orthogonal Procrustes Analysis and Individual Differences Scaling. The polar (or dual) cone representation, corresponding to inner-products around a centroid, is also discussed. Some new characterisations of distance cones in terms of circumhyperspheres are presented.

Item Type:	Book Chapter
ISBN:	3-540-73558-5, 978-3-540-73558-8
Academic Unit/Department:	Mathematics, Computing and Technology Mathematics, Computing and Technology > Mathematics and Statistics
Item ID:	9766
Depositing User:	Casper Albers
Date Deposited:	08 Oct 2007
Last Modified:	02 Dec 2010 20:05
URI:	http://oro.open.ac.uk/id/eprint/9766

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