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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