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.

DOI: https://doi.org/10.1007/978-3-540-73560-1_41

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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About

• Item ORO ID
• 9766
• Item Type
• Book Section
• ISBN
• 3-540-73558-5, 978-3-540-73558-8
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM)
  Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
• Depositing User
• Casper Albers