Comments on "On Approximating Euclidean Metrics by Weighted t-Cost Distances in Arbitrary Dimension"
arXiv:1206.2061 · doi:10.1016/j.patrec.2012.03.002
Abstract
Mukherjee (Pattern Recognition Letters, vol. 32, pp. 824-831, 2011) recently introduced a class of distance functions called weighted t-cost distances that generalize m-neighbor, octagonal, and t-cost distances. He proved that weighted t-cost distances form a family of metrics and derived an approximation for the Euclidean norm in . In this note we compare this approximation to two previously proposed Euclidean norm approximations and demonstrate that the empirical average errors given by Mukherjee are significantly optimistic in . We also propose a simple normalization scheme that improves the accuracy of his approximation substantially with respect to both average and maximum relative errors.
arXiv comment7 pages, 1 figure, 3 tables. arXiv admin note: substantial text overlap with arXiv:1008.4870