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August, 1992 Multilinear Models: Applications in Spectroscopy
Sue Leurgans, Robert T. Ross
Statist. Sci. 7(3): 289-310 (August, 1992). DOI: 10.1214/ss/1177011225


Multilinear models are models in which the expectation of a multiway array is the sum of products of parameters, where each parameter is associated with only one of the ways. In spectroscopy, multilinear models permit mathematical decompositions of data sets when chemical decomposition of specimens is difficult or impossible. This paper presents a unified description of the models in an array notation. The spectroscopic context shows how to interpret one initialization of the nonlinear least-squares fits of these models. Several examples show that these models can be applied successfully.


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Sue Leurgans. Robert T. Ross. "Multilinear Models: Applications in Spectroscopy." Statist. Sci. 7 (3) 289 - 310, August, 1992.


Published: August, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0955.62592
MathSciNet: MR1181414
Digital Object Identifier: 10.1214/ss/1177011225

Keywords: Multi-mode factor analysis , nonlinear least-squares , PARAFAC , three-way arrays

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.7 • No. 3 • August, 1992
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