Department of Environmental Biology and Fisheries Science, National Taiwan Ocean University, 2 Pei-Ning Road, Keelung 20224, Taiwan.
Comput Methods Programs Biomed. 2011 Dec;104(3):382-96. doi: 10.1016/j.cmpb.2010.12.003. Epub 2011 Jan 5.
Both sample entropy and approximate entropy are measurements of complexity. The two methods have received a great deal of attention in the last few years, and have been successfully verified and applied to biomedical applications and many others. However, the algorithms proposed in the literature require O(N(2)) execution time, which is not fast enough for online applications and for applications with long data sets. To accelerate computation, the authors of the present paper have developed a new algorithm that reduces the computational time to O(N(3/2))) using O(N) storage. As biomedical data are often measured with integer-type data, the computation time can be further reduced to O(N) using O(N) storage. The execution times of the experimental results with ECG, EEG, RR, and DNA signals show a significant improvement of more than 100 times when compared with the conventional O(N(2)) method for N=80,000 (N=length of the signal). Furthermore, an adaptive version of the new algorithm has been developed to speed up the computation for short data length. Experimental results show an improvement of more than 10 times when compared with the conventional method for N>4000.
样本熵和近似熵都是衡量复杂性的方法。这两种方法在过去几年中受到了广泛关注，并已成功验证并应用于生物医学应用和许多其他领域。然而，文献中提出的算法需要 O(N(2))的执行时间，对于在线应用程序和具有长数据集的应用程序来说，这不够快。为了加速计算，本文的作者开发了一种新算法，该算法使用 O(N)的存储空间将计算时间减少到 O(N(3/2)))。由于生物医学数据通常使用整数类型的数据进行测量，因此使用 O(N)的存储空间可以将计算时间进一步减少到 O(N)。与 N=80,000（N=信号长度）时的传统 O(N(2))方法相比，ECG、EEG、RR 和 DNA 信号的实验结果的执行时间有了显著提高，超过 100 倍。此外，还开发了一种新算法的自适应版本，以加快短数据长度的计算。与传统方法相比，当 N>4000 时，实验结果提高了 10 倍以上。
