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Convergence Properties of an Iterative Procedure of Ipsatizing and Standardizing a Data Matrix, with Applications to Parafac/Candecomp Preprocessing

Published online by Cambridge University Press:  01 January 2025

Jos M. F. ten Berge  and
Henk A. L. Kiers
Jos M. F. ten Berge*
Affiliation:
University of Groningen
Henk A. L. Kiers
Affiliation:
University of Groningen
*
Requests for reprints should be sent to Jos M. F. ten Berge, Department of Psychology, University of Groningen, Grote Markt 32, 9712 HV Groningen, THE NETHERLANDS.
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Abstract

Centering a matrix row-wise and rescaling it column-wise to a unit sum of squares requires an iterative procedure. It is shown that this procedure converges to a stable solution. This solution need not be centered row-wise if the limiting point of the interations is a matrix of rank one. The results of the present paper bear directly on several types of preprocessing methods in Parafac/Candecomp.

Keywords

ipsative datadoubly standardized matrices
Type
Original Paper
Information
Psychometrika , Volume 54 , Issue 2 , June 1989 , pp. 231 - 235
Copyright
Copyright © 1989 The Psychometric Society

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References

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