Journal of Classification

, Volume 4, Issue 2, pp 175–190 | Cite as

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

  • M. W. Browne
Authors Of Articles

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.

Keywords

Classical scaling ELEGANT algorithm Newton-Raphson Squared distances 

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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • M. W. Browne
    • 1
  1. 1.Department of StatisticsUniversity of South AfricaPretoriaSouth Africa

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