Piek Albert B, Stolz Inga, Keller Karsten
Institute of Mathematics, University of Lübeck, D-23562 Lübeck, Germany.
Graduate School for Computing in Medicine and Life Sciences, University of Lübeck, D-23562 Lübeck, Germany.
Entropy (Basel). 2019 May 29;21(6):547. doi: 10.3390/e21060547.
The study of nonlinear and possibly chaotic time-dependent systems involves long-term data acquisition or high sample rates. The resulting big data is valuable in order to provide useful insights into long-term dynamics. However, efficient and robust algorithms are required that can analyze long time series without decomposing the data into smaller series. Here symbolic-based analysis techniques that regard the dependence of data points are of some special interest. Such techniques are often prone to capacity or, on the contrary, to undersampling problems if the chosen parameters are too large. In this paper we present and apply algorithms of the relatively new ordinal symbolic approach. These algorithms use overlapping information and binary number representation, whilst being fast in the sense of algorithmic complexity, and allow, to the best of our knowledge, larger parameters than comparable methods currently used. We exploit the achieved large parameter range to investigate the limits of entropy measures based on ordinal symbolics. Moreover, we discuss data simulations from this viewpoint.
对非线性且可能具有混沌特性的时变系统的研究涉及长期数据采集或高采样率。由此产生的大数据对于深入了解长期动态特性很有价值。然而，需要高效且稳健的算法，能够在不将数据分解为较小序列的情况下分析长时间序列。在此，基于符号的分析技术，即考虑数据点之间的依赖性，具有特殊意义。如果所选参数过大，此类技术往往容易出现容量问题，或者相反，容易出现欠采样问题。在本文中，我们介绍并应用相对较新的序数符号方法的算法。这些算法使用重叠信息和二进制数表示，在算法复杂度方面速度很快，并且据我们所知，与目前使用的可比方法相比，允许使用更大的参数。我们利用所实现的大参数范围来研究基于序数符号的熵度量的极限。此外，我们从这个角度讨论数据模拟。
