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Group average representations in Euclidean distance cones. (English) Zbl 1154.15312
Brito, Paula (ed.) et al., Selected contributions in data analysis and classification. In honour of Edwin Diday. With a foreword by Yves Escoufier. Berlin: Springer (ISBN 978-3-540-73558-8/pbk). Studies in Classification, Data Analysis, and Knowledge Organization, 445-454 (2007).
Summary: 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.
For the entire collection see [Zbl 1146.68003].

MSC:
15B57 Hermitian, skew-Hermitian, and related matrices
15B48 Positive matrices and their generalizations; cones of matrices
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