Extensions of Classical Multidimensional Scaling via Variable Reduction

Michael W. Trosset
Additional contact information
Michael W. Trosset: College of William & Mary

Computational Statistics, 2002, vol. 17, issue 2, No 1, 147-163

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.

Keywords: Classical Multidimensional Scaling; Variance Reduction; Distance Matrix Completion Problem; Trosset; Application-specific Constraints (search for similar items in EconPapers)
Date: 2002
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s001800200099 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:compst:v:17:y:2002:i:2:d:10.1007_s001800200099

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/180/PS2

DOI: 10.1007/s001800200099

Access Statistics for this article

Computational Statistics is currently edited by Wataru Sakamoto, Ricardo Cao and Jürgen Symanzik

More articles in Computational Statistics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().