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The optimality of the centroid method

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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.

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Authors and Affiliations

  1. Départment de Mathématiques et de Statistique, Université de Moncton, and Moncton, N.B., E1A 3E9, Canada

    Vartan Choulakian

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  1. Vartan Choulakian
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Correspondence to Vartan Choulakian.

Additional information

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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Choulakian, V. The optimality of the centroid method. Psychometrika 68, 473–475 (2003). https://doi.org/10.1007/BF02294738

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  • DOI: https://doi.org/10.1007/BF02294738

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