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The Integration of Multidimensional Scaling and Multivariate Analysis with Optimal Transformations

Published online by Cambridge University Press:  01 January 2025

Jacqueline J. Meulman
Jacqueline J. Meulman*
Affiliation:
Department of Data Theory, University of Leiden
*
Requests for reprints should be sent to Jacqueline J. Meulman, Department of Data Theory, Faculty of Social Sciences, University of Leiden, PO Box 9555, 2300 RB Leiden, THE NETHERLANDS.
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Abstract

The recent history of multidimensional data analysis suggests two distinct traditions that have developed along quite different lines. In multidimensional scaling (MDS), the available data typically describe the relationships among a set of objects in terms of similarity/dissimilarity (or (pseudo-)distances). In multivariate analysis (MVA), data usually result from observation on a collection of variables over a common set of objects. This paper starts from a very general multidimensional scaling task, defined on distances between objects derived from one or more sets of multivariate data. Particular special cases of the general problem, following familiar notions from MVA, will be discussed that encompass a variety of analysis techniques, including the possible use of optimal variable transformation. Throughout, it will be noted how certain data analysis approaches are equivalent to familiar MVA solutions when particular problem specifications are combined with particular distance approximations.

Keywords

multivariate analysismultidimensional scalingnonlinear transformationsdistance approximationmajorization
Type
Original Paper
Information
Psychometrika , Volume 57 , Issue 4 , December 1992 , pp. 539 - 565
Copyright
Copyright © 1992 The Psychometric Society

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Footnotes

This research was supported by the Royal Netherlands Academy of Arts and Sciences (KNAW). An earlier version of this paper was written during a stay at McGill University in Montréal; this visit was supported by a travel grant from the Netherlands Organization for Scientific Research (NWO). I am grateful to Jim Ramsay and Willem Heiser for their encouragement and helpful suggestions, and to the Editor and referees for their constructive comments.

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