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Extensions of Classical Multidimensional Scaling via Variable Reduction

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  • Michael W. Trosset

    (College of William & Mary)

Abstract

Summary Classical multidimensional scaling constructs a configuration of points that minimizes a certain measure of discrepancy between the configuration’s interpoint distance matrix and a fixed dissimilarity matrix. Recent extensions have replaced the fixed dissimilarity matrix with a closed and convex set of dissimilarity matrices. These formulations replace fixed dissimilarities with optimization variables (disparities) that are permitted to vary subject to application-specific constraints. For example, simple bound constraints are suitable for distance matrix completion problems (Trosset, 2000) and for inferring molecular conformation from information about interatomic distances (Trosset, 1998b); whereas order constraints are suitable for nonmetric multidimensional scaling (Trosset, 1998a). This paper describes the computational theory that provides a common foundation for these formulations.

Suggested Citation

  • Michael W. Trosset, 2002. "Extensions of Classical Multidimensional Scaling via Variable Reduction," Computational Statistics, Springer, vol. 17(2), pages 147-163, July.
    • Handle: RePEc:spr:compst:v:17:y:2002:i:2:d:10.1007_s001800200099
    DOI: 10.1007/s001800200099
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    Cited by:

    1. Malone, Samuel W. & Tarazaga, Pablo & Trosset, Michael W., 2002. "Better initial configurations for metric multidimensional scaling," Computational Statistics & Data Analysis, Elsevier, vol. 41(1), pages 143-156, November.
    2. Herden, Gerhard & Pallack, Andreas, 2005. "Adequateness and interpretability of objective functions in ordinal data analysis," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 19-69, May.
    3. Lewis, R.M. & Trosset, M.W., 2006. "Sensitivity analysis of the strain criterion for multidimensional scaling," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 135-153, January.

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