Minimum Hausdorff distance under rigid motions and comparison of protein structures |
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Authors: | Banghe Li Bo Li Yuefeng Shen |
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Institution: | (1) School of Mechanical Engineering, University of Leeds, Leeds, LS2 9JT, UK;(2) School of Computing, University of Leeds, Leeds, LS2 9JT, UK |
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Abstract: | Hausdorff distance between two compact sets, defined as the maximum distance from a point of one set to another set, has many
application in computer science. It is a good measure for the similarity of two sets. This paper proves that the shape distance
between two compact sets in R
n
defined by minimum Hausdorff distance under rigid motions is a distance. The authors introduce similarity comparison problems
in protein science, and propose that this measure may have good application to comparison of protein structure as well. For
calculation of this distance, the authors give one dimensional formulas for problems (2, n), (3, 3), and (3, 4). These formulas can reduce time needed for solving these problems. The authors did some numerical experiments
for (2, n). On these sets of data, this formula can reduce time needed to one fifteenth of the best algorithms known on average. As
n increases, it would save more time. |
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Keywords: | |
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