Detection of the permutation symmetry in pattern sets
Symmetry is a powerful tool to reduce the freedom degrees of a system. But the applicability of the symmetry tool strongly depends on the ability to calculate the symmetries of the system. There exists an interesting algorithmic problem to search for the symmetry of a high-dimensional system. In thi...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/DDNS/2006/81503 |
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| _version_ | 1849683083841765376 |
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| author | Dong Ji-Yang Zhang Jun-Ying |
| author_facet | Dong Ji-Yang Zhang Jun-Ying |
| author_sort | Dong Ji-Yang |
| collection | DOAJ |
| description | Symmetry is a powerful tool to reduce the freedom degrees of a
system. But the applicability of the symmetry tool strongly
depends on the ability to calculate the symmetries of the system.
There exists an interesting algorithmic problem to search
for the symmetry of a high-dimensional system. In this
paper, a genetic algorithm-based permutation symmetry detection
approach is proposed for pattern set. Firstly, the permutation
symmetry distance (PSD) is defined to measure the similarity of a
pattern set before and after being transformed by a
permutation operator. Secondly, the permutation symmetry detection
problem is converted into an optimization problem by taking the
PSD as a fitness function. Lastly, a genetic algorithm-based
approach is designed for the symmetry detection problem. Computer
simulation results are also given for five pattern sets of
different dimensionality, which show the efficiency and
speediness of the proposed detection approach, especially in
high-dimensional cases. |
| format | Article |
| id | doaj-art-c9d3bc13afbd47ce9120d7da98ac71f2 |
| institution | DOAJ |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-c9d3bc13afbd47ce9120d7da98ac71f22025-08-20T03:23:59ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2006-01-01200610.1155/DDNS/2006/8150381503Detection of the permutation symmetry in pattern setsDong Ji-Yang0Zhang Jun-Ying1Department of Physics, Xiamen University, Xiamen, Fujian 361005, ChinaNational Key Lab for Radar Signal Processing, Xidian University, Xi'an, Shaanxi 710071, ChinaSymmetry is a powerful tool to reduce the freedom degrees of a system. But the applicability of the symmetry tool strongly depends on the ability to calculate the symmetries of the system. There exists an interesting algorithmic problem to search for the symmetry of a high-dimensional system. In this paper, a genetic algorithm-based permutation symmetry detection approach is proposed for pattern set. Firstly, the permutation symmetry distance (PSD) is defined to measure the similarity of a pattern set before and after being transformed by a permutation operator. Secondly, the permutation symmetry detection problem is converted into an optimization problem by taking the PSD as a fitness function. Lastly, a genetic algorithm-based approach is designed for the symmetry detection problem. Computer simulation results are also given for five pattern sets of different dimensionality, which show the efficiency and speediness of the proposed detection approach, especially in high-dimensional cases.http://dx.doi.org/10.1155/DDNS/2006/81503 |
| spellingShingle | Dong Ji-Yang Zhang Jun-Ying Detection of the permutation symmetry in pattern sets Discrete Dynamics in Nature and Society |
| title | Detection of the permutation symmetry in pattern sets |
| title_full | Detection of the permutation symmetry in pattern sets |
| title_fullStr | Detection of the permutation symmetry in pattern sets |
| title_full_unstemmed | Detection of the permutation symmetry in pattern sets |
| title_short | Detection of the permutation symmetry in pattern sets |
| title_sort | detection of the permutation symmetry in pattern sets |
| url | http://dx.doi.org/10.1155/DDNS/2006/81503 |
| work_keys_str_mv | AT dongjiyang detectionofthepermutationsymmetryinpatternsets AT zhangjunying detectionofthepermutationsymmetryinpatternsets |