Bi-Lipschitz embeddings into low-dimensional Euclidean spaces

Jiří Matoušek

Commentationes Mathematicae Universitatis Carolinae (1990)

  • Volume: 031, Issue: 3, page 589-600
  • ISSN: 0010-2628

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Matoušek, Jiří. "Bi-Lipschitz embeddings into low-dimensional Euclidean spaces." Commentationes Mathematicae Universitatis Carolinae 031.3 (1990): 589-600. <http://eudml.org/doc/17879>.

@article{Matoušek1990,
author = {Matoušek, Jiří},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Euclidean space; finite metric spaces; distortion; Lipschitz distance},
language = {eng},
number = {3},
pages = {589-600},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Bi-Lipschitz embeddings into low-dimensional Euclidean spaces},
url = {http://eudml.org/doc/17879},
volume = {031},
year = {1990},
}

TY - JOUR
AU - Matoušek, Jiří
TI - Bi-Lipschitz embeddings into low-dimensional Euclidean spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1990
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 031
IS - 3
SP - 589
EP - 600
LA - eng
KW - Euclidean space; finite metric spaces; distortion; Lipschitz distance
UR - http://eudml.org/doc/17879
ER -

References

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  8. Ganea T., Comment on embedding of polyhedra in Euclidean spaces, Bull. Acad. Polon. Sci. SOr. Sci. Math. Astronom. Phys. 7 (1959), 27-32. (1959) Zbl0123.39804MR0102079
  9. Heiser W. J., Multidimensional scaling with least absolute residuals, in: Classification and related methods of data analysis, H. H. Bock ed., North Holland (1988), 455-472. (1988) 
  10. Johnson W., Lindenstrauss J., Extensions of Lipschitz maps into a Hilbert space, Contemp. Math. 26 (1984), 189-206. (1984) Zbl0539.46017MR0737400
  11. Johnson W. B., Lindenstrauss J., Schechtman G., On Lipschitz embedding of finite metric spaces in low dimensional normed spaces, in: Geometrical aspects of functional analysis, (J. Lindenstrauss, V. D. Milman eds.), LNM 1267, Springer-Verlag 1987. (1987) Zbl0631.46016MR0907694
  12. Kruskal J. B., Multidimensional scaling by optimizing goodness-of-fit to a nonmetric hypothesis, Psychometrika 29 (1964), 1-27. (1964) Zbl0123.36803MR0169712
  13. Mathar R., The best Euclidian fit to a given distance matrix in prescribed dimension, Lin. Alg. Appl. 6T (1985), 1-6. (1985) Zbl0569.15015MR0787361
  14. Matoušek J., Lipschitz distance of metric spaces, CSc. degree thesis (in Czech), Charles University 1989. (1989) 
  15. Mardešić S., Segal J., A note on polyhedra embeddable in the plane, Michig. Math. J. 33 (1966), 633-638. (1966) Zbl0168.21602MR0199848
  16. Mardešić S., Segal J., e-mappxngs and generalized manifolds, Michig. Math. J. 14 (1967), 171-182. (1967) Zbl0152.21704MR0211407
  17. Milman V. D., Schechtman G., Asymptotic theory of finite dimensional normed spaces, LNM 1200, Springer-Verlag 1986. (1986) Zbl0606.46013MR0856576
  18. Schoenberg I. J., Metric spaces and positive definite functions, Trans. Amer. Math. Soc. 44 (1938), 522-536. (1938) Zbl0019.41502MR1501980
  19. Wells J. H., Williams L. R., Embeddings and extensions in analysis, Springer-Verlag 1975. (1975) Zbl0324.46034MR0461107

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