Get 20M+ Full-Text Papers For Less Than $1.50/day. Subscribe now for You or Your Team.

Learn More →

Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis

Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis Abstract Multidimensional scaling is the problem of representingn objects geometrically byn points, so that the interpoint distances correspond in some sense to experimental dissimilarities between objects. In just what sense distances and dissimilarities should correspond has been left rather vague in most approaches, thus leaving these approaches logically incomplete. Our fundamental hypothesis is that dissimilarities and distances are monotonically related. We define a quantitative, intuitively satisfying measure of goodness of fit to this hypothesis. Our technique of multidimensional scaling is to compute that configuration of points which optimizes the goodness of fit. A practical computer program for doing the calculations is described in a companion paper. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Psychometrika Springer Journals

Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis

Psychometrika , Volume 29 (1): 27 – Mar 1, 1964

Loading next page...
 
/lp/springer-journals/multidimensional-scaling-by-optimizing-goodness-of-fit-to-a-nonmetric-mzWMlqWVx0

References (24)

Publisher
Springer Journals
Copyright
1964 Psychometric Society
ISSN
0033-3123
eISSN
1860-0980
DOI
10.1007/BF02289565
Publisher site
See Article on Publisher Site

Abstract

Abstract Multidimensional scaling is the problem of representingn objects geometrically byn points, so that the interpoint distances correspond in some sense to experimental dissimilarities between objects. In just what sense distances and dissimilarities should correspond has been left rather vague in most approaches, thus leaving these approaches logically incomplete. Our fundamental hypothesis is that dissimilarities and distances are monotonically related. We define a quantitative, intuitively satisfying measure of goodness of fit to this hypothesis. Our technique of multidimensional scaling is to compute that configuration of points which optimizes the goodness of fit. A practical computer program for doing the calculations is described in a companion paper.

Journal

PsychometrikaSpringer Journals

Published: Mar 1, 1964

There are no references for this article.