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Non‐triviality and identification of a constrained Tucker3 analysis
Author(s) -
ten Berge Jos M. F.,
Smilde Age K.
Publication year - 2002
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.760
Subject(s) - triviality , uniqueness , constraint (computer aided design) , simple (philosophy) , identification (biology) , core (optical fiber) , zero (linguistics) , mathematics , computer science , mathematical analysis , geometry , philosophy , linguistics , biology , botany , epistemology , telecommunications
Properties of estimated parameters of models of chemical systems are important. This paper focuses on two properties of such estimated parameters: triviality and uniqueness. If a chemical system is analyzed using a Tucker3 model, then the resulting core can often be rotated to a simple structure containing zeros. This means that it is possible that a prespecified pattern of zero and non‐zero elements of the core, as used in e.g. constrained Tucker3 models, is not an active constraint; that is, the zeros can be obtained trivially for free. Once a non‐trivial pattern of zeros in the core is specified, the question arises whether this pattern is sufficient for obtaining unique loadings. Both issues are discussed in this paper and it is shown that the model used by Gurden et al. ( J. Chemometrics 2001; 15: 101–121) does essentially involve a non‐trivial core and implies rotationally unique parameter estimates. Copyright © 2002 John Wiley & Sons, Ltd.