The Assumption of Proportional Components when Candecomp is Applied to Symmetric Matrices in the Context of Indscal

The use of Candecomp to fit scalar products in the context of INDSCAL is based on the assumption that the symmetry of the data matrices involved causes the component matrices to be equal when Candecomp converges. Ten Berge and Kiers gave examples where this assumption is violated for Gramian data ma...

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Detalles Bibliográficos
Autores principales: Dosse, Mohammed Bennani, Berge, Jos M. F.
Formato: Texto
Lenguaje:English
Publicado: Springer-Verlag 2008
Materias:
Theory and Methods
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2798989/
https://www.ncbi.nlm.nih.gov/pubmed/20046850
http://dx.doi.org/10.1007/s11336-007-9044-x
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author Dosse, Mohammed Bennani
Berge, Jos M. F.
author_facet Dosse, Mohammed Bennani
Berge, Jos M. F.
author_sort Dosse, Mohammed Bennani
collection PubMed
description The use of Candecomp to fit scalar products in the context of INDSCAL is based on the assumption that the symmetry of the data matrices involved causes the component matrices to be equal when Candecomp converges. Ten Berge and Kiers gave examples where this assumption is violated for Gramian data matrices. These examples are believed to be local minima. It is now shown that, in the single-component case, the assumption can only be violated at saddle points. Chances of Candecomp converging to a saddle point are small but still nonzero.
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spelling pubmed-27989892009-12-29 The Assumption of Proportional Components when Candecomp is Applied to Symmetric Matrices in the Context of Indscal Dosse, Mohammed Bennani Berge, Jos M. F. Psychometrika Theory and Methods The use of Candecomp to fit scalar products in the context of INDSCAL is based on the assumption that the symmetry of the data matrices involved causes the component matrices to be equal when Candecomp converges. Ten Berge and Kiers gave examples where this assumption is violated for Gramian data matrices. These examples are believed to be local minima. It is now shown that, in the single-component case, the assumption can only be violated at saddle points. Chances of Candecomp converging to a saddle point are small but still nonzero. Springer-Verlag 2008-01-25 2008 /pmc/articles/PMC2798989/ /pubmed/20046850 http://dx.doi.org/10.1007/s11336-007-9044-x Text en © The Author(s) 2008 https://creativecommons.org/licenses/by-nc/4.0/This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
spellingShingle Theory and Methods
Dosse, Mohammed Bennani
Berge, Jos M. F.
The Assumption of Proportional Components when Candecomp is Applied to Symmetric Matrices in the Context of Indscal
title The Assumption of Proportional Components when Candecomp is Applied to Symmetric Matrices in the Context of Indscal
title_full The Assumption of Proportional Components when Candecomp is Applied to Symmetric Matrices in the Context of Indscal
title_fullStr The Assumption of Proportional Components when Candecomp is Applied to Symmetric Matrices in the Context of Indscal
title_full_unstemmed The Assumption of Proportional Components when Candecomp is Applied to Symmetric Matrices in the Context of Indscal
title_short The Assumption of Proportional Components when Candecomp is Applied to Symmetric Matrices in the Context of Indscal
title_sort assumption of proportional components when candecomp is applied to symmetric matrices in the context of indscal
topic Theory and Methods
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2798989/
https://www.ncbi.nlm.nih.gov/pubmed/20046850
http://dx.doi.org/10.1007/s11336-007-9044-x
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