, Volume 49, Issue 3, pp 391-402

Upper bounds for Kruskal's stress

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Abstract

In this paper the relationships between the two formulas for stress proposed by Kruskal in 1964 are studied. It is shown that stress formula one has a system of nontrivial upper bounds. It seems likely that minimization of this loss function will be liable to produce solutions for which this upper bound is small. These are regularly shaped configurations. Even though stress formula two yields less equivocal results, it seems to be expected that minimization of this loss function will tend to produce configurations in which the points are clumped. These results give no clue as to which of the two loss functions is to be preferred.

This study has been supported by the Nederlandse Organisatie voor Zuiver-Wetenschappelijk Onderzoek (Netherlands Organization for the Advancement of Pure Research), under grant 56-146.
Comments by Willem Heiser and Frank Critichley have been very helpful.
The second author presently is employed by the Netherlands Central Bureau of Statistics, Voorburg.