Comments on 'On approximating Euclidean metrics by weighted t-cost distances in arbitrary dimension'
| Autor: | Fatih Celiker, Hassan A. Kingravi, M. Emre Celebi |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
FOS: Computer and information sciences
Normalization (statistics) I.5 Computer Vision and Pattern Recognition (cs.CV) Dimension (graph theory) Computer Science - Computer Vision and Pattern Recognition G.1.2 02 engineering and technology Euclidean distance matrix Combinatorics Artificial Intelligence Simple (abstract algebra) Euclidean geometry FOS: Mathematics 0202 electrical engineering electronic engineering information engineering Mathematics Discrete mathematics Computer Science - Numerical Analysis 020206 networking & telecommunications Numerical Analysis (math.NA) Weighted Voronoi diagram Euclidean distance Signal Processing Pattern recognition (psychology) 020201 artificial intelligence & image processing Computer Vision and Pattern Recognition Software |
| Zdroj: | Pattern Recognition Letters. 33:1422-1425 |
| ISSN: | 0167-8655 |
| DOI: | 10.1016/j.patrec.2012.03.002 |
| Popis: | 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. 7 pages, 1 figure, 3 tables. arXiv admin note: substantial text overlap with arXiv:1008.4870 |
| Databáze: | OpenAIRE |
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