A novel method to identify the scaling region of correlation dimension
文献类型:期刊论文
作者 | Zhou Shuang1,2; Feng Yong1![]() ![]() |
刊名 | ACTA PHYSICA SINICA
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出版日期 | 2015-07-05 |
卷号 | 64期号:13页码:6 |
关键词 | Correlation Dimension Scaling Region Fractal Fuzzy Clustering |
ISSN号 | 1000-3290 |
DOI | 10.7498/aps.64.130504 |
其他题名 | 一种识别关联维数无标度区间的新方法 |
英文摘要 | A random fractal exhibits self-similarity over the scaling region, this is different from the regular fractal. The scaling region obtained by the proper method for the exact fractal dimension is very important. And the correlation dimension is one of the fractal dimensions which is used widely in many fields. Therefore, it is necessary and timely to identify the scaling region that plays a critical role in calculating the correlation dimension accurately in various chaotic systems. Visual identification is widely used to determine the scaling region as a quick and simple subjective method. However, this method may lead to an inaccurate result in Grassberger Procaccia algorithm. In order to reduce the error caused by human factors from computing the correlation dimension, a novel method of identifying the scaling region based on simulated annealing genetic fuzzy C-means clustering algorithm is proposed. This new method is based on the fluctuating characteristics that the second-order derivative of the curve within the scaling region is zero or nearly zero. Firstly, the second-order differential of the double logarithm correlation integral discrete data is calculated. Secondly, the simulated annealing genetic fuzzy C-means clustering method is used for dividing the data into three groups: positive fluctuation data, zero fluctuation data, and negative fluctuation data. The zero fluctuation data are selected to retain, the rest is excluded. Thirdly, the 3 sigma criteria are used for excluding gross errors to retain those valid from the zero fluctuation data. Fourthly, the data of the consecutive nature point interval are chosen from the retained data. Finally, the regression analysis and statistical test are used to identify the scaling region from the data valid. In order to verify the effectiveness of the proposed method, it is used to simulate the Lorenz and Henon systems. The calculated results are in good agreement with the theoretical values. Experimental results show that the proposed new approach is easy to operate, more efficient and more accurate than the subjective recognition, K-means method, and 2-means method in identifying the scaling region. |
资助项目 | National Natural Science Foundation of China[11301524] ; Chongqing Science and Technology Key Project, China[cstc2012ggB40004] ; CAS western light program |
WOS研究方向 | Physics |
语种 | 英语 |
WOS记录号 | WOS:000357674600004 |
出版者 | CHINESE PHYSICAL SOC |
源URL | [http://119.78.100.138/handle/2HOD01W0/1786] ![]() |
专题 | 自动推理与认知研究中心 |
作者单位 | 1.Chinese Acad Sci, Chongqing Inst Green & Intelligent Technol, Chongqing Key Lab Automated Reasoning & Cognit, Chongqing 400714, Peoples R China 2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China |
推荐引用方式 GB/T 7714 | Zhou Shuang,Feng Yong,Wu Wen-Yuan. A novel method to identify the scaling region of correlation dimension[J]. ACTA PHYSICA SINICA,2015,64(13):6. |
APA | Zhou Shuang,Feng Yong,&Wu Wen-Yuan.(2015).A novel method to identify the scaling region of correlation dimension.ACTA PHYSICA SINICA,64(13),6. |
MLA | Zhou Shuang,et al."A novel method to identify the scaling region of correlation dimension".ACTA PHYSICA SINICA 64.13(2015):6. |
入库方式: OAI收割
来源:重庆绿色智能技术研究院
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