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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.

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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: 14 Jan 2016 16:47
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