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

A. P. Zubarev ()
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A. P. Zubarev: Samara State University of Railway Transport

Journal of Classification, 2017, vol. 34, issue 3, No 2, 366-383

Abstract: 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.

Keywords: Ultrametric space; High dimension data; Degree of ultrametricity; Law of large numbers (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s00357-017-9236-8

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