Measuring complexity using FuzzyEn, ApEn, and SampEn
Measuring complexity using FuzzyEn, ApEn, and SampEn
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DOI：
10.1016/j.medengphy.2008.04.005
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发表时间：
2009-01-01
影响因子：
2.2
通讯作者：
Wang, Zhizhong
中科院分区：
文献类型：
--
作者：
Chen, Weiting;Zhuang, Jun;Wang, Zhizhong
本文比较了三种相关的复杂性度量，ApEn、SampEn和FuzzyEn。由于ApEn和SampEn中向量的相似性是基于Heaviside函数的硬敏感边界来定义的，所以这两类统计量对参数选择的敏感性较高，在参数较小的情况下可能无效。引入模糊集的概念，提出了一种新的度量方法FuzzyEn，其中基于模糊隶属函数和向量形状的模糊相似度来定义向量的相似度。模糊函数的软边界和连续边界保证了模糊函数在小参数下的连续性和有效性。FuzzyEn函数获得的更多细节也使得它比ApEn和SampEn更准确地定义了熵。此外，基于向量形状的相似度定义，以及对自匹配的排除，使得FuzzyEn的相对一致性更强，对数据长度的依赖性更小。理论分析和实验结果表明，该方法能够更好地评估信号复杂度，更方便、更有效地应用于受噪声污染的短时间序列。(c) 2008年合同。Elsevier Ltd.出版。版权所有。
This paper compares three related measures of complexity, ApEn, SampEn, and FuzzyEn. Since vectors' similarity is defined on the basis of the hard and sensitive boundary of Heaviside function in ApEn and SampEn, the two families of statistics show high sensitivity to the parameter selection and may be invalid in case of small parameter. Importing the concept of fuzzy sets, we developed a new measure FuzzyEn, where vectors' similarity is defined by fuzzy similarity degree based on fuzzy membership functions and vectors' shapes. The soft and continuous boundaries of fuzzy functions ensure the continuity as well as the validity of FuzzyEn at small parameters. The more details obtained by fuzz), functions also make FuzzyEn a more accurate entropy definition than ApEn and SampEn. In addition, similarity definition based on vectors' shapes, together with the exclusion of self-matches, earns FuzzyEn stronger relative consistency and less dependence on data length. Both theoretical analysis and experimental results show that FuzzyEn provides an improved evaluation of signal complexity and can be more conveniently and powerfully applied to short time series contaminated by noise. (C) 2008 IPEM. Published by Elsevier Ltd. All rights reserved.