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: Dong Ji-Yang, Zhang Jun-Ying
Format: Article
Language:English
Published: Wiley 2006-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/DDNS/2006/81503
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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
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language English
publishDate 2006-01-01
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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