Psychometrika

, Volume 29, Issue 2, pp 115–129 | Cite as

Nonmetric multidimensional scaling: A numerical method

  • J. B. Kruskal
Article

Abstract

We describe the numerical methods required in our approach to multi-dimensional scaling. The rationale of this approach has appeared previously.

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References

  1. [1]
    Barton, D. E. and Mallows, C. L. The randomization bases of the amalgamation of weighted means.J. roy. statist. Soc., Series B, 1961,23, 423–433.Google Scholar
  2. [2]
    Bartholomew, D. J. A test of homogeneity for ordered alternatives.Biometrika, 1959,46, 36–48.CrossRefGoogle Scholar
  3. [3]
    Bartholomew, D. J. A test of homogeneity of means under restricted alternatives (with discussion).J. roy. statist. Soc., Series B, 1961,23, 239–281.Google Scholar
  4. [4]
    Hardy, G. H., Littlewood, J. E., and Polya, G.Inequalities. (2nd ed.) Cambridge, Eng.: Cambridge Univ. Press, 1952.Google Scholar
  5. [5]
    Hildebrandt, P. and Isbitz H. Radix-exchange—An internal sorting method for digital computers.J. Assoc. computing Machinery, 1959,6, 156–163.CrossRefGoogle Scholar
  6. [6]
    Kolmogorov, A. N. and Fomin, S. V.Elements of the theory of functions and functional analysis. Vol. 1.Metric and normed spaces. Translated from the first (1954) Russian Edition by Leo F. Boron, Rochester, N. Y., Graylock Press, 1957.Google Scholar
  7. [7]
    Kruskal, J. Multidimensional scaling by optimizing goodness-of-fit to a nonmetric hypothesis.Psychometrika, 1964,29, 1–28.CrossRefGoogle Scholar
  8. [8]
    Miles, R. E. The complete amalgamation into blocks, by weighted means, of a finite set of real numbers.Biometrika, 1959,46, 317–327.CrossRefGoogle Scholar
  9. [9]
    Shepard, R. N. The analysis of proximities: Multidimensional scaling with an unknown distance function.Psychometrika (I and II), 1962,27, 125–139, 219–246.CrossRefGoogle Scholar
  10. [10]
    Spang, H. A. III. A review of minimization techniques for nonlinear functions.SIAM Rev., 1962,4, 343–365.CrossRefGoogle Scholar
  11. [11]
    van Eeden, C. Maximum likelihood estimation of partially or completely ordered parameters, I.Proc. Akademie van Wetenschappen, Series A, 1957,60, 128–136.Google Scholar
  12. [12]
    van Eeden, C. Note on two methods for estimating ordered parameters of probability distributions.Proc. Akademie van Wetenschappen, Series A, 1957,60, 506–512.Google Scholar

Copyright information

© Psychometric Society 1964

Authors and Affiliations

  • J. B. Kruskal
    • 1
  1. 1.Bell Telephone LaboratoriesUSA

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