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The problem of the additive constant and eigenvalues in metric multidimensional scaling

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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.

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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 Murray Hill, NJ: Bell Laboratories, unpublished.

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Authors and Affiliations

  1. Japan Univac Research Institute, Japan

    Takayuki Saito

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  1. Takayuki Saito
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Additional information

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.

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Saito, T. The problem of the additive constant and eigenvalues in metric multidimensional scaling. Psychometrika 43, 193–201 (1978). https://doi.org/10.1007/BF02293862

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  • DOI: https://doi.org/10.1007/BF02293862

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