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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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