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The Problem of the Additive Constant and Eigenvalues in Metric Multidimensional Scaling

Published online by Cambridge University Press:  01 January 2025

Takayuki Saito
Takayuki Saito*
Affiliation:
Japan Univac Research Institute
*
Requests for reprints should be sent to Takayuki Saito, Misawa 979-230 A 127, Hino-shi, Tokyo 191, Japan.
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Abstract

This paper is concerned with the additive constant problem in metric multidimensional scaling. First the influence of the additive constant on eigenvalues of a scalar product matrix is discussed. The second part of this paper is devoted to the introduction of a new formulation of the additive constant problem. A solution is given for fixed dimensionality, by maximizing a normalized index of fit with a gradient method. An experimental computation has shown that the author's solution is accurate and easy to follow.

Keywords

additive constant problemeigenvaluesmetric multidimensional scalingnormalized index of fit
Type
Original Paper
Information
Psychometrika , Volume 43 , Issue 2 , June 1978 , pp. 193 - 201
Copyright
Copyright © 1978 The Psychometric Society

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Footnotes

The author wishes to thank Mr. Yukio Inukai and anonymous reviewers for their useful suggestions. Sincere thanks are extended to Dr. Yajiro Morita who improved the English manuscript.

References

Reference Note

De Leeuw, J. Finding a positive semidefinite matrix of prescribed rank r in a nonlinear differentiable manifold (Technical Report). Murray Hill, NJ: Bell Laboratories, unpublished.Google Scholar

References

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