The equivalence of Tucker3 and Parafac models with two components

P. M. Kroonenberg; J. M. F. ten Berge

doi:10.1016/j.chemolab.2010.05.022

The equivalence of Tucker3 and Parafac models with two components

P. M. Kroonenberg^*
, J. M. F. ten Berge

^*Corresponding author for this work

Psychometrics and Statistics

Research output: Contribution to journal › Article › Academic › peer-review

14 Citations (Scopus)

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Abstract

This study investigates similarities and differences between Tucker3 models with two components for each mode and Parafac models with two components. If the core array of the 2 x 2 x 2 Tucker3 model is of rank 2 the solutions contain exactly the same information, but they do not when the rank of the core array is three. Two illustrative applications show the effect the different core arrays have on the solutions and their interpretability. (C) 2010 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	21-26
Number of pages	6
Journal	Chemometrics and Intelligent Laboratory Systems
Volume	106
Issue number	1
DOIs	https://doi.org/10.1016/j.chemolab.2010.05.022
Publication status	Published - 15-Mar-2011

Keywords

Parafac model
Tucker3 model
Two-component models
Degeneracy
Rank-two core array
Rank-three core array
ARRAYS
DEGENERACY

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The equivalence of Tucker3 and Parafac models with two componentsFinal publisher's version, 537 KBLicence: Taverne

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title = "The equivalence of Tucker3 and Parafac models with two components",

abstract = "This study investigates similarities and differences between Tucker3 models with two components for each mode and Parafac models with two components. If the core array of the 2 x 2 x 2 Tucker3 model is of rank 2 the solutions contain exactly the same information, but they do not when the rank of the core array is three. Two illustrative applications show the effect the different core arrays have on the solutions and their interpretability. (C) 2010 Elsevier B.V. All rights reserved.",

keywords = "Parafac model, Tucker3 model, Two-component models, Degeneracy, Rank-two core array, Rank-three core array, ARRAYS, DEGENERACY",

author = "Kroonenberg, \{P. M.\} and \{ten Berge\}, \{J. M. F.\}",

year = "2011",

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AU - ten Berge, J. M. F.

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N2 - This study investigates similarities and differences between Tucker3 models with two components for each mode and Parafac models with two components. If the core array of the 2 x 2 x 2 Tucker3 model is of rank 2 the solutions contain exactly the same information, but they do not when the rank of the core array is three. Two illustrative applications show the effect the different core arrays have on the solutions and their interpretability. (C) 2010 Elsevier B.V. All rights reserved.

AB - This study investigates similarities and differences between Tucker3 models with two components for each mode and Parafac models with two components. If the core array of the 2 x 2 x 2 Tucker3 model is of rank 2 the solutions contain exactly the same information, but they do not when the rank of the core array is three. Two illustrative applications show the effect the different core arrays have on the solutions and their interpretability. (C) 2010 Elsevier B.V. All rights reserved.

KW - Parafac model

KW - Tucker3 model

KW - Two-component models

KW - Degeneracy

KW - Rank-two core array

KW - Rank-three core array

KW - ARRAYS

KW - DEGENERACY

U2 - 10.1016/j.chemolab.2010.05.022

DO - 10.1016/j.chemolab.2010.05.022

M3 - Article

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EP - 26

JO - Chemometrics and Intelligent Laboratory Systems

JF - Chemometrics and Intelligent Laboratory Systems

IS - 1

ER -

The equivalence of Tucker3 and Parafac models with two components

Abstract

Keywords

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