APPLICATIONS OF CONVEX ANALYSIS TO MULTIDIMENSIONAL SCALING

@inproceedings{Leeuw2000APPLICATIONSOC,
  title={APPLICATIONS OF CONVEX ANALYSIS TO MULTIDIMENSIONAL SCALING},
  author={Jan de Leeuw},
  year={2000}
}
In this paper we discuss the convergence of an algorithm for metric and nonmetric multidimensional scaling that is very similar to the C-matrix algorithm of Guttman. The paper improves some earlier results in two respects. In the first place the analysis is extended to cover general Minkovski metrics, in the second place a more elementary proof of convergence based on results of Robert is presented. 

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References

Publications referenced by this paper.
SHOWING 1-10 OF 23 REFERENCES

Calcul du Maximum d'une Forme Quadratique Définie Positive sur la Boule Unité de ψ ∞

Tao Pham Dinh
  • MDS AND CONVEX ANALYSIS
  • 1976

Sufficient Conditions for the Convergence of Monotonic Mathematical Programming Algorithms

R R Meyer
  • Journal of Computer and System Sciences
  • 1976

Eléments Homoduaux d'une Matrice A Relatifs a un Couple de Normes (φ, ψ)

Tao Pham Dinh
  • Eléments Homoduaux d'une Matrice A Relatifs a un Couple de Normes (φ, ψ)
  • 1975

A Mathematical and Empirical Analysis of Two Multidimensional Scaling Algorithms

J C Lingoes, E E Roskam
  • Psychometrika
  • 1973

The Approximate Minimization of Functionals

J W Daniel
  • The Approximate Minimization of Functionals
  • 1971

Convex Analysis

  • Princeton Landmarks in Mathematics and Physics
  • 1970