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

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  • J. T. Temple

    (Royal Botanic Gardens Kew)

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 → ∞.

Suggested Citation

  • J. T. Temple, 2023. "Characteristics of Distance Matrices Based on Euclidean, Manhattan and Hausdorff Coefficients," Journal of Classification, Springer;The Classification Society, vol. 40(2), pages 214-232, July.
    • Handle: RePEc:spr:jclass:v:40:y:2023:i:2:d:10.1007_s00357-023-09435-1
    DOI: 10.1007/s00357-023-09435-1
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    References listed on IDEAS

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    1. J. Gower & P. Legendre, 1986. "Metric and Euclidean properties of dissimilarity coefficients," Journal of Classification, Springer;The Classification Society, vol. 3(1), pages 5-48, March.
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