Convergence of the sequence of parameters generated by alternating least squares algorithms

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Several models in data analysis are estimated by minimizing the objective function defined as the residual sum of squares between the model and the data. A necessary and sufficient condition for the existence of a least squares estimator is that the objective function attains its infimum at a unique point. It is shown that the objective function for Parafac-2 need not attain its infimum, and that of DEDICOM, constrained Parafac-2, and, under a weak assumption, SCA and Dynamals do attain their infimum. Furthermore, the sequence of parameter vectors, generated by an alternating least squares algorithm, converges if it decreases the objective function to its infimum which is attained at one or finitely many points.
Original languageEnglish
Pages (from-to)481-489
JournalComputational statistics and data analysis
Volume51
Issue number2
DOIs
Publication statusPublished - 15 Nov 2006

Keywords

  • data analysis

Cite this

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title = "Convergence of the sequence of parameters generated by alternating least squares algorithms",
abstract = "Several models in data analysis are estimated by minimizing the objective function defined as the residual sum of squares between the model and the data. A necessary and sufficient condition for the existence of a least squares estimator is that the objective function attains its infimum at a unique point. It is shown that the objective function for Parafac-2 need not attain its infimum, and that of DEDICOM, constrained Parafac-2, and, under a weak assumption, SCA and Dynamals do attain their infimum. Furthermore, the sequence of parameter vectors, generated by an alternating least squares algorithm, converges if it decreases the objective function to its infimum which is attained at one or finitely many points.",
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author = "Krijnen, {Wim P.}",
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language = "English",
volume = "51",
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journal = "Computational statistics and data analysis",
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publisher = "Elsevier",
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Convergence of the sequence of parameters generated by alternating least squares algorithms. / Krijnen, Wim P.

In: Computational statistics and data analysis, Vol. 51, No. 2, 15.11.2006, p. 481-489.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Convergence of the sequence of parameters generated by alternating least squares algorithms

AU - Krijnen, Wim P.

PY - 2006/11/15

Y1 - 2006/11/15

N2 - Several models in data analysis are estimated by minimizing the objective function defined as the residual sum of squares between the model and the data. A necessary and sufficient condition for the existence of a least squares estimator is that the objective function attains its infimum at a unique point. It is shown that the objective function for Parafac-2 need not attain its infimum, and that of DEDICOM, constrained Parafac-2, and, under a weak assumption, SCA and Dynamals do attain their infimum. Furthermore, the sequence of parameter vectors, generated by an alternating least squares algorithm, converges if it decreases the objective function to its infimum which is attained at one or finitely many points.

AB - Several models in data analysis are estimated by minimizing the objective function defined as the residual sum of squares between the model and the data. A necessary and sufficient condition for the existence of a least squares estimator is that the objective function attains its infimum at a unique point. It is shown that the objective function for Parafac-2 need not attain its infimum, and that of DEDICOM, constrained Parafac-2, and, under a weak assumption, SCA and Dynamals do attain their infimum. Furthermore, the sequence of parameter vectors, generated by an alternating least squares algorithm, converges if it decreases the objective function to its infimum which is attained at one or finitely many points.

KW - data analysis

KW - data-analyse

U2 - 10.1016/j.csda.2005.09.003

DO - 10.1016/j.csda.2005.09.003

M3 - Article

VL - 51

SP - 481

EP - 489

JO - Computational statistics and data analysis

JF - Computational statistics and data analysis

SN - 0167-9473

IS - 2

ER -