Characteristics of Distance Matrices Based on Euclidean, Manhattan and Hausdorff Coefficients

J. T. Temple
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J. T. Temple: Royal Botanic Gardens Kew

Journal of Classification, 2023, vol. 40, issue 2, No 2, 214-232

Abstract: Abstract From n-size samples of k-variate points, we construct n × n distance-matrices based on the widely used Euclidean, Manhattan and Hausdorff coefficients and study (individually and in pairs) their properties P, R and ρ using theoretical analysis and both computer-generated and empirical data. The concordance PEM is shown by analysis of uniformly-distributed data to decrease asymptotically as k → ∞ to exp [‒ exp [‒ γ]] ≅ 0.5704, and PEH and PMH to decrease to zero, as also in generated N(0,1) and empirical data. In geological data, PEM is higher than predicted for 10 0.9 and independent of k for both U(0,1) and N(0,1); ρEH and ρEM decline to zero as k → ∞.

Keywords: Concordance; Correlation; Distance matrices; Euclidean; Euler’s Gamma; Exp [‒ exp [‒ γ]]; Hausdorff; k-variate points; Manhattan; Nearest-neighbour; Properties; Robustness (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00357-023-09435-1

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