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The Assumption of Proportional Components when Candecomp is Applied to Symmetric Matrices in the Context of Indscal

Published online by Cambridge University Press:  01 January 2025

Mohammed Bennani Dosse  and
Jos M. F. Berge
Mohammed Bennani Dosse*
Affiliation:
University of Rennes 2
Jos M. F. Berge
Affiliation:
University of Groningen
*
Requests for reprints should be sent to Mohammed Bennani Dosse, Statistics Research Team, University of Rennes 2, Rennes, France. E-mail: [email protected]
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Abstract

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The use of Candecomp to fit scalar products in the context of INDSCAL is based on the assumption that the symmetry of the data matrices involved causes the component matrices to be equal when Candecomp converges. Ten Berge and Kiers gave examples where this assumption is violated for Gramian data matrices. These examples are believed to be local minima. It is now shown that, in the single-component case, the assumption can only be violated at saddle points. Chances of Candecomp converging to a saddle point are small but still nonzero.

Keywords

CandecompParafacIndscal
Type
Theory and Methods
Information
Psychometrika , Volume 73 , Issue 2 , June 2008 , pp. 303 - 307
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NC
Open AccessThis is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Copyright
Copyright © 2008 The Author(s)

References

Carroll, J.D., & Chang, J.J. (1970). Analysis of individual differences in multidimensional scaling via an n-way generalization of Eckart-Young decomposition. Psychometrika, 35, 283–319.CrossRefGoogle Scholar
Ten Berge, J.M.F., & Kiers, H.A.L. (1991). Some clarifications of the Candecomp algorithm applied to Indscal. Psychometrika, 56, 317–326.CrossRefGoogle Scholar