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Universal optimality of rank constrained matrix approximation. (English) Zbl 0817.62055

Bock, Hans-Hermann (ed.) et al., Information systems and data analysis. Prospects, foundations, applications. Proceedings of the 17th annual conference of the Gesellschaft für Klassifikation e. V., Univ. of Kaiserslautern, Germany, March 3-5, 1993. Berlin: Springer-Verlag. 332-339 (1994).
Summary: The major results of this paper consist of an extension of optimality properties concerning the best rank-\(r\) matrix approximation, and of the solution of classical multidimensional scaling (MDS), in either case from the class of orthogonally invariant norms to a wider class of approximation criteria. Observing that many problems in multivariate analysis exhibit symmetries under a group of transformations, and, furthermore, realizing the relevance of preorderings for matrix approximation problems in multivariate statistics and MDS, leads to a natural approach towards proving universal optimality of their solution via invariant preorderings of matrices.
For the entire collection see [Zbl 0812.00033].

MSC:

62H99 Multivariate analysis
62A01 Foundations and philosophical topics in statistics
91C15 One- and multidimensional scaling in the social and behavioral sciences
15A99 Basic linear algebra
62-06 Proceedings, conferences, collections, etc. pertaining to statistics
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