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.
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Albers, C.J., Critchley, F., Gower, J.C. (2007). Group Average Representations in Euclidean Distance Cones. In: Brito, P., Cucumel, G., Bertrand, P., de Carvalho, F. (eds) Selected Contributions in Data Analysis and Classification. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73560-1_41
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DOI: https://doi.org/10.1007/978-3-540-73560-1_41
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73558-8
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