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An Upper Bound for Sstress

Published online by Cambridge University Press:  01 January 2025

Jan de Leeuw  and
Bert Bettonvil
Jan de Leeuw*
Affiliation:
Department of Data Theory FSW, University of Leiden
Bert Bettonvil
Affiliation:
Department of Data Theory FSW, University of Leiden
*
Requests for reprints should be sent to Jan de Leeuw, Department of Data Theory FSW/RUL, Middelstegracht 4, 2312 TW Leiden, THE NETHERLANDS.
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Abstract

In this note we derive an upper bound for the minimum for the multidimensional scaling loss function sstress. We conjecture that minimum sstress solution will be biased towards regular positioning of clumps of points over the surface of a sphere.

Keywords

Nonmetric scalingmultidimensional scalingloss functionsdistance geometry
Type
Notes and Comments
Information
Psychometrika , Volume 51 , Issue 1 , March 1986 , pp. 149 - 153
Copyright
Copyright © 1986 The Psychometric Society

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Footnotes

This study has been supported by the Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek (Netherlands Organization for the Advancement of Pure Research) under grant 56–97.

References

de Leeuw, J., Stoop, I. (1984). Upper bounds for Kruskal's stress. Psychometrika, 49, 391–402.CrossRefGoogle Scholar
Takane, Y., Young, F. W., de Leeuw, J. (1977). Nonmetric individual differences scaling: An alternating least squares method with optimal scaling features. Psychometrika, 42, 7–68.CrossRefGoogle Scholar