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

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 P EM is shown by analysis of uniformly-distributed data to decrease asymptotically as k → ∞ to exp [‒ exp [‒ γ]] ≅ 0.5704, and P EH and P MH to decrease to zero, as also in generated N (0,1) and empirical data. In geological data, P EM is higher than predicted for 10