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Simplicity and typical rank of three‐way arrays, with applications to Tucker‐3 analysis with simple cores
Author(s) -
ten Berge Jos M. F.
Publication year - 2004
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.840
Subject(s) - simplicity , simple (philosophy) , rank (graph theory) , uniqueness , basis (linear algebra) , core (optical fiber) , computer science , principal component analysis , algorithm , mathematics , theoretical computer science , artificial intelligence , combinatorics , geometry , telecommunications , mathematical analysis , philosophy , epistemology
In chemometric applications of Tucker three‐way principal component analysis, core arrays are often constrained to have a large majority of zero elements. This gives rise to questions of non‐triviality (are the constraints active, or can any core of a given format be transformed to satisfy the constraints?) and uniqueness (can we transform the components in one or more directions without losing the given pattern of zero elements in the core?). Rather than deciding such questions on an ad hoc basis, general principles are to be preferred. This paper gives an overview of simplicity transformations on the one hand, and typical rank results on the other, which are suitable to determine whether or not certain constrained cores are trivial. Copyright © 2004 John Wiley & Sons, Ltd.