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Differentiability of Kruskal's Stress at a Local Minimum

Published online by Cambridge University Press:  01 January 2025

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

It is shown that Kruskal's multidimensional scaling loss function is differentiable at a local minimum. Or, to put it differently, that in multidimensional scaling solutions using Kruskal's stress distinct points cannot coincide.

Keywords

multidimensional scalingloss functions
Type
Original Paper
Information
Psychometrika , Volume 49 , Issue 1 , March 1984 , pp. 111 - 113
Copyright
Copyright © 1984 The Psychometric Society

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References

Reference Notes

De Leeuw, J. (1974). Smoothness properties of nonmetric loss functions. Unpublished paper, Bell Telephone Labs.Google Scholar
De Leeuw, J. (1981). Linear convergence of multidimensional scaling algorithms. Unpublished paper, Department of Data Theory, Leiden University.Google Scholar

References

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