An improved majorization algorithm for Robust Procrustes analysis

Patrick J.F. Groenen; Patrizia Giaquinto; Henk A.L. Kiers

doi:10.1007/3-540-27373-5_18

An improved majorization algorithm for Robust Procrustes analysis

Patrick J.F. Groenen
, Patrizia Giaquinto
, Henk A.L. Kiers

University of Bari Aldo Moro
University of Groningen

Research output: Chapter/Conference proceeding › Conference proceeding › Academic › peer-review

3 Citations (Scopus)

Abstract

In this paper, we focus on algorithms for Robust Procrustes Analysis that are used to rotate a solution of coordinates towards a target solution while controlling outliers. Verboon (1994) and Verboon and Heiser (1992) showed how iterative weighted least-squares can be used to solve the problem. Kiers (1997) improved upon their algorithm by using iterative majorization. In this paper, we propose a new method called “weighted majorization” that improves on the method by Kiers (1997). A simulation study shows that compared to the method by Kiers (1997), the solutions obtained by weighted majorization are in almost all cases of better quality and are obtained significantly faster.

Original language	English
Title of host publication	Studies in Classification, Data Analysis, and Knowledge Organization
Editors	Maurizio Vichi, Paola Monari, Stefania Mignani, Angela Montanari
Publisher	Springer Science+Business Media
Pages	151-158
Number of pages	8
Edition	211289
ISBN (Print)	9783319557076, 9783319557229, 9783540238096
DOIs	https://doi.org/10.1007/3-540-27373-5_18
Publication status	Published - 2005
Event	Biannual meeting of the Classification and Data Analysis Group of the Italian Statistical Society, CLADAG 2003 - Bologna, Italy Duration: 22 Sept 2003 → 24 Sept 2003

Publication series

Series	Studies in Classification, Data Analysis, and Knowledge Organization
Number	211289
Volume	0
ISSN	1431-8814

Conference

Conference	Biannual meeting of the Classification and Data Analysis Group of the Italian Statistical Society, CLADAG 2003
Country/Territory	Italy
City	Bologna
Period	22/09/03 → 24/09/03

Bibliographical note

Publisher Copyright:
© 2005, Springer-Verlag. Heidelberg 2005.

Access to Document

10.1007/3-540-27373-5_18

Cite this

Groenen, Patrick J.F. ; Giaquinto, Patrizia ; Kiers, Henk A.L. / An improved majorization algorithm for Robust Procrustes analysis. Studies in Classification, Data Analysis, and Knowledge Organization. editor / Maurizio Vichi ; Paola Monari ; Stefania Mignani ; Angela Montanari. 211289. ed. Springer Science+Business Media, 2005. pp. 151-158 (Studies in Classification, Data Analysis, and Knowledge Organization; No. 211289, Vol. 0).

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abstract = "In this paper, we focus on algorithms for Robust Procrustes Analysis that are used to rotate a solution of coordinates towards a target solution while controlling outliers. Verboon (1994) and Verboon and Heiser (1992) showed how iterative weighted least-squares can be used to solve the problem. Kiers (1997) improved upon their algorithm by using iterative majorization. In this paper, we propose a new method called “weighted majorization” that improves on the method by Kiers (1997). A simulation study shows that compared to the method by Kiers (1997), the solutions obtained by weighted majorization are in almost all cases of better quality and are obtained significantly faster.",

author = "Groenen, \{Patrick J.F.\} and Patrizia Giaquinto and Kiers, \{Henk A.L.\}",

note = "Publisher Copyright: {\textcopyright} 2005, Springer-Verlag. Heidelberg 2005.; Biannual meeting of the Classification and Data Analysis Group of the Italian Statistical Society, CLADAG 2003 ; Conference date: 22-09-2003 Through 24-09-2003",

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Groenen, PJF, Giaquinto, P & Kiers, HAL 2005, An improved majorization algorithm for Robust Procrustes analysis. in M Vichi, P Monari, S Mignani & A Montanari (eds), Studies in Classification, Data Analysis, and Knowledge Organization. 211289 edn, Springer Science+Business Media, Studies in Classification, Data Analysis, and Knowledge Organization, no. 211289, vol. 0, pp. 151-158, Biannual meeting of the Classification and Data Analysis Group of the Italian Statistical Society, CLADAG 2003, Bologna, Italy, 22/09/03. https://doi.org/10.1007/3-540-27373-5_18

An improved majorization algorithm for Robust Procrustes analysis. / Groenen, Patrick J.F.; Giaquinto, Patrizia; Kiers, Henk A.L.
Studies in Classification, Data Analysis, and Knowledge Organization. ed. / Maurizio Vichi; Paola Monari; Stefania Mignani; Angela Montanari. 211289. ed. Springer Science+Business Media, 2005. p. 151-158 (Studies in Classification, Data Analysis, and Knowledge Organization; No. 211289, Vol. 0).

Research output: Chapter/Conference proceeding › Conference proceeding › Academic › peer-review

TY - GEN

T1 - An improved majorization algorithm for Robust Procrustes analysis

AU - Groenen, Patrick J.F.

AU - Giaquinto, Patrizia

AU - Kiers, Henk A.L.

PY - 2005

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N2 - In this paper, we focus on algorithms for Robust Procrustes Analysis that are used to rotate a solution of coordinates towards a target solution while controlling outliers. Verboon (1994) and Verboon and Heiser (1992) showed how iterative weighted least-squares can be used to solve the problem. Kiers (1997) improved upon their algorithm by using iterative majorization. In this paper, we propose a new method called “weighted majorization” that improves on the method by Kiers (1997). A simulation study shows that compared to the method by Kiers (1997), the solutions obtained by weighted majorization are in almost all cases of better quality and are obtained significantly faster.

AB - In this paper, we focus on algorithms for Robust Procrustes Analysis that are used to rotate a solution of coordinates towards a target solution while controlling outliers. Verboon (1994) and Verboon and Heiser (1992) showed how iterative weighted least-squares can be used to solve the problem. Kiers (1997) improved upon their algorithm by using iterative majorization. In this paper, we propose a new method called “weighted majorization” that improves on the method by Kiers (1997). A simulation study shows that compared to the method by Kiers (1997), the solutions obtained by weighted majorization are in almost all cases of better quality and are obtained significantly faster.

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SN - 9783319557229

SN - 9783540238096

T3 - Studies in Classification, Data Analysis, and Knowledge Organization

SP - 151

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BT - Studies in Classification, Data Analysis, and Knowledge Organization

A2 - Vichi, Maurizio

A2 - Monari, Paola

A2 - Mignani, Stefania

A2 - Montanari, Angela

PB - Springer Science+Business Media

T2 - Biannual meeting of the Classification and Data Analysis Group of the Italian Statistical Society, CLADAG 2003

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Groenen PJF, Giaquinto P, Kiers HAL. An improved majorization algorithm for Robust Procrustes analysis. In Vichi M, Monari P, Mignani S, Montanari A, editors, Studies in Classification, Data Analysis, and Knowledge Organization. 211289 ed. Springer Science+Business Media. 2005. p. 151-158. (Studies in Classification, Data Analysis, and Knowledge Organization; No. 211289, Vol. 0). doi: 10.1007/3-540-27373-5_18

An improved majorization algorithm for Robust Procrustes analysis

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