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Computational Statistics

, Volume 17, Issue 2, pp 147–163 | Cite as

Extensions of Classical Multidimensional Scaling via Variable Reduction

  • Michael W. Trosset
Article

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.

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Copyright information

© Physica-Verlag 2002

Authors and Affiliations

  • Michael W. Trosset
    • 1
  1. 1.Department of MathematicsCollege of William & MaryWilliamsburgUSA

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