Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Comments on "On Approximating Euclidean Metrics by Weighted t-Cost
  Distances in Arbitrary Dimension"   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 $\mathbb{Z}^n$. 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
$\mathbb{R}^n$. We also propose a simple normalization scheme that improves the
accuracy of his approximation substantially with respect to both average and
maximum relative errors.

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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
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The categories of this paper are: physics
0
The categories of this paper are: hep-ph
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The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat