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


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.


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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