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The Young-Householder algorithm and the least squares multidimensional scaling of squared distances

The Young-Householder algorithm and the least squares multidimensional scaling of squared distances It is shown that replacement of the zero diagonal elements of the symmetric data matrix of approximate squared distances by certain other quantities in the Young-Householder algorithm will yield a least squares fit to squared distances instead of to scalar products. Iterative algorithms for obtaining these replacement diagonal elements are described and relationships with the ELEGANT algorithm (de Leeuw 1975; Takane 1977) are discussed. In “large residual” situations a penalty function approach, motivated by the ELEGANT algorithm, is adopted. Empirical comparisons of the algorithms are given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Classification Springer Journals

The Young-Householder algorithm and the least squares multidimensional scaling of squared distances

Browne, M.
Journal of Classification , Volume 4 (2) – Jun 18, 2005
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References (12)

Publisher
Springer Journals
Copyright
Copyright © 1987 by Springer-Verlag
Subject
Statistics; Statistical Theory and Methods; Pattern Recognition; Bioinformatics; Signal,Image and Speech Processing; Psychometrics; Marketing
ISSN
0176-4268
eISSN
1432-1343
DOI
10.1007/BF01896985
Publisher site
See Article on Publisher Site

Abstract

It is shown that replacement of the zero diagonal elements of the symmetric data matrix of approximate squared distances by certain other quantities in the Young-Householder algorithm will yield a least squares fit to squared distances instead of to scalar products. Iterative algorithms for obtaining these replacement diagonal elements are described and relationships with the ELEGANT algorithm (de Leeuw 1975; Takane 1977) are discussed. In “large residual” situations a penalty function approach, motivated by the ELEGANT algorithm, is adopted. Empirical comparisons of the algorithms are given.

Journal

Journal of Classification – Springer Journals

Published: Jun 18, 2005

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