Assessment of Time Series Complexity Using Improved Approximate Entropy
KONG De-Ren1, XIE Hong-Bo2**
1School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094 2School of Electronic and Information Engineering, Jiangsu University, Zhenjiang 212013
Assessment of Time Series Complexity Using Improved Approximate Entropy
KONG De-Ren1, XIE Hong-Bo2**
1School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094 2School of Electronic and Information Engineering, Jiangsu University, Zhenjiang 212013
摘要Approximate entropy (ApEn), a measure quantifying complexity and/or regularity, is believed to be an effective method of analyzing diverse settings. However, the similarity definition of vectors based on Heaviside function may cause some problems in the validity and accuracy of ApEn. To overcome the problems, an improved approximate entropy (iApEn) based on the sigmoid function is proposed. The performance of iApEn is tested on the independent identically distributed (IID) Gaussian noise, the MIX stochastic model, the Rossler map, the logistic map, and the high-dimensional Mackey–Glass oscillator. The results show that iApEn is superior to ApEn in several aspects, including better relative consistency, freedom of parameter selection, robust to noise, and more independence on record length when characterizing time series with different complexities.
Abstract：Approximate entropy (ApEn), a measure quantifying complexity and/or regularity, is believed to be an effective method of analyzing diverse settings. However, the similarity definition of vectors based on Heaviside function may cause some problems in the validity and accuracy of ApEn. To overcome the problems, an improved approximate entropy (iApEn) based on the sigmoid function is proposed. The performance of iApEn is tested on the independent identically distributed (IID) Gaussian noise, the MIX stochastic model, the Rossler map, the logistic map, and the high-dimensional Mackey–Glass oscillator. The results show that iApEn is superior to ApEn in several aspects, including better relative consistency, freedom of parameter selection, robust to noise, and more independence on record length when characterizing time series with different complexities.
KONG De-Ren;XIE Hong-Bo**
. Assessment of Time Series Complexity Using Improved Approximate Entropy[J]. 中国物理快报, 2011, 28(9): 90502-090502.
KONG De-Ren, XIE Hong-Bo**
. Assessment of Time Series Complexity Using Improved Approximate Entropy. Chin. Phys. Lett., 2011, 28(9): 90502-090502.
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2011, Vol. 28 
