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.



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.

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