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The Young-Householder algorithm and the least squares multidimensional scaling of squared distances (1987)

Browne, M. W.

Springer

Journal of classification 4 (1987), S. 175-190

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ISSN: 1432-1343

Keywords: Classical scaling ; ELEGANT algorithm ; Newton-Raphson ; Squared distances

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01896985

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