Publication

Some New Results on Orthogonally Constrained Candecomp

Bennani Dosse, M., ten Berge, J. M. F. & Tendeiro, J. N., Jul-2011, In : Journal of Classification. 28, 2, p. 144-155 12 p.

Research output: Contribution to journalArticleAcademicpeer-review

APA

Bennani Dosse, M., ten Berge, J. M. F., & Tendeiro, J. N. (2011). Some New Results on Orthogonally Constrained Candecomp. Journal of Classification, 28(2), 144-155. https://doi.org/10.1007/s00357-011-9086-8

Author

Bennani Dosse, Mohammed ; ten Berge, Jos M. F. ; Tendeiro, Jorge N. / Some New Results on Orthogonally Constrained Candecomp. In: Journal of Classification. 2011 ; Vol. 28, No. 2. pp. 144-155.

Harvard

Bennani Dosse, M, ten Berge, JMF & Tendeiro, JN 2011, 'Some New Results on Orthogonally Constrained Candecomp', Journal of Classification, vol. 28, no. 2, pp. 144-155. https://doi.org/10.1007/s00357-011-9086-8

Standard

Some New Results on Orthogonally Constrained Candecomp. / Bennani Dosse, Mohammed; ten Berge, Jos M. F.; Tendeiro, Jorge N.

In: Journal of Classification, Vol. 28, No. 2, 07.2011, p. 144-155.

Research output: Contribution to journalArticleAcademicpeer-review

Vancouver

Bennani Dosse M, ten Berge JMF, Tendeiro JN. Some New Results on Orthogonally Constrained Candecomp. Journal of Classification. 2011 Jul;28(2):144-155. https://doi.org/10.1007/s00357-011-9086-8


BibTeX

@article{0a9a0a7bd50147e79973e344954d8781,
title = "Some New Results on Orthogonally Constrained Candecomp",
abstract = "The use of Candecomp to fit scalar products in the context of Indscal is based on the assumption that, due to the symmetry of the data matrices involved, two components matrices will become equal when Candecomp converges. Bennani Dosse and Ten Berge (2008) have shown that, in the single component case, the assumption can only be violated at saddle points in the case of Gramian matrices. This paper again considers Candecomp applied to symmetric matrices, but with an orthonormality constraint on the components. This constrained version of Candecomp, when applied to symmetric matrices, has long been known under the acronym Indort. When the data matrices are positive definite, or have become positive semidefinite due to double centering, and the saliences are nonnegative - by chance or by constraint -, the component matrices resulting from Indort are shown to be equal. Because Indort is also free from so-called degeneracy problems, it is a highly attractive alternative to Candecomp in the present context. We also consider a well-known successive approach to the orthogonally constrained Indscal problem and we compare, from simulated and real data sets, its results with those given by the simultaneous (Indort) approach.",
keywords = "Simultaneous approach, Successive approach, Indort, Three-way Data, Candecomp, Indscal, COMMON COMPONENTS, RANK",
author = "{Bennani Dosse}, Mohammed and {ten Berge}, {Jos M. F.} and Tendeiro, {Jorge N.}",
year = "2011",
month = "7",
doi = "10.1007/s00357-011-9086-8",
language = "English",
volume = "28",
pages = "144--155",
journal = "Journal of Classification",
issn = "0176-4268",
publisher = "SPRINGER",
number = "2",

}

RIS

TY - JOUR

T1 - Some New Results on Orthogonally Constrained Candecomp

AU - Bennani Dosse, Mohammed

AU - ten Berge, Jos M. F.

AU - Tendeiro, Jorge N.

PY - 2011/7

Y1 - 2011/7

N2 - The use of Candecomp to fit scalar products in the context of Indscal is based on the assumption that, due to the symmetry of the data matrices involved, two components matrices will become equal when Candecomp converges. Bennani Dosse and Ten Berge (2008) have shown that, in the single component case, the assumption can only be violated at saddle points in the case of Gramian matrices. This paper again considers Candecomp applied to symmetric matrices, but with an orthonormality constraint on the components. This constrained version of Candecomp, when applied to symmetric matrices, has long been known under the acronym Indort. When the data matrices are positive definite, or have become positive semidefinite due to double centering, and the saliences are nonnegative - by chance or by constraint -, the component matrices resulting from Indort are shown to be equal. Because Indort is also free from so-called degeneracy problems, it is a highly attractive alternative to Candecomp in the present context. We also consider a well-known successive approach to the orthogonally constrained Indscal problem and we compare, from simulated and real data sets, its results with those given by the simultaneous (Indort) approach.

AB - The use of Candecomp to fit scalar products in the context of Indscal is based on the assumption that, due to the symmetry of the data matrices involved, two components matrices will become equal when Candecomp converges. Bennani Dosse and Ten Berge (2008) have shown that, in the single component case, the assumption can only be violated at saddle points in the case of Gramian matrices. This paper again considers Candecomp applied to symmetric matrices, but with an orthonormality constraint on the components. This constrained version of Candecomp, when applied to symmetric matrices, has long been known under the acronym Indort. When the data matrices are positive definite, or have become positive semidefinite due to double centering, and the saliences are nonnegative - by chance or by constraint -, the component matrices resulting from Indort are shown to be equal. Because Indort is also free from so-called degeneracy problems, it is a highly attractive alternative to Candecomp in the present context. We also consider a well-known successive approach to the orthogonally constrained Indscal problem and we compare, from simulated and real data sets, its results with those given by the simultaneous (Indort) approach.

KW - Simultaneous approach

KW - Successive approach

KW - Indort

KW - Three-way Data

KW - Candecomp

KW - Indscal

KW - COMMON COMPONENTS

KW - RANK

U2 - 10.1007/s00357-011-9086-8

DO - 10.1007/s00357-011-9086-8

M3 - Article

VL - 28

SP - 144

EP - 155

JO - Journal of Classification

JF - Journal of Classification

SN - 0176-4268

IS - 2

ER -

ID: 2117697