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The Optimality of the Centroid Method

Published online by Cambridge University Press:  01 January 2025

Vartan Choulakian
Vartan Choulakian*
Affiliation:
Départment de Mathématiques et de Statistique, Université de Moncton
*
Requests for reprints should be sent to Vartan Choulakian, Départment de Mathématiques et de Statistique, Université de Moncton, and Moncton, N.B., CANADA E1A 3E9. E-Mail: choulav@umoncton.ca
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Abstract

The aim of this note is to show that the centroid method has two optimality properties. It yields loadings with the highest sum of absolute values, even in absence of the constraint that the squared component weights be equal. In addition, it yields scores with maximum variance, subject to the constraint that none of the squared component weights be larger than 1.

Keywords

principal component analysis
Type
Article
Information
Psychometrika , Volume 68 , Issue 3 , September 2003 , pp. 473 - 475
Copyright
Copyright © 2003 The Psychometric Society

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Footnotes

This research is financed by NSERC of Canada. The author is grateful to Michel Tenenhaus for pointing the similarity of the procedures in the centroid method and Q-mode PCA in L1. The author also thanks the editor and associate editor for providing shorter proofs of the theorems, along with the referees for their helpful comments.

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