On the Ultrametric Generated by Random Distribution of Points in Euclidean Spaces of Large Dimensions with Correlated Coordinates

On the Ultrametric Generated by Random Distribution of Points in Euclidean Spaces of Large... Recently a general theorem stating that the matrix of normalized Euclidean distances on the set of specially distributed random points in the n-dimensional Euclidean space ℝ n with independent coordinates converges in probability as n→∞ to the ultrametric matrix had been proved. The main theorem of the present paper extends this result to the case of weakly correlated coordinates of random points. Prior to formulating and stating this result we give two illustrative examples describing particular algorithms of generation of such nearly ultrametric spaces. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Classification Springer Journals

On the Ultrametric Generated by Random Distribution of Points in Euclidean Spaces of Large Dimensions with Correlated Coordinates

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Publisher
Springer US
Copyright
Copyright © 2017 by Classification Society of North America
Subject
Statistics; Statistical Theory and Methods; Pattern Recognition; Bioinformatics; Signal,Image and Speech Processing; Psychometrics; Marketing
ISSN
0176-4268
eISSN
1432-1343
D.O.I.
10.1007/s00357-017-9236-8
Publisher site
See Article on Publisher Site

Abstract

Recently a general theorem stating that the matrix of normalized Euclidean distances on the set of specially distributed random points in the n-dimensional Euclidean space ℝ n with independent coordinates converges in probability as n→∞ to the ultrametric matrix had been proved. The main theorem of the present paper extends this result to the case of weakly correlated coordinates of random points. Prior to formulating and stating this result we give two illustrative examples describing particular algorithms of generation of such nearly ultrametric spaces.

Journal

Journal of ClassificationSpringer Journals

Published: Sep 30, 2017

References

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