Effect of extreme data loss on long-range correlated and anticorrelated signals quantified by detrended fluctuation analysis.
Effect of extreme data loss on long-range correlated and anticorrelated signals quantified by detrended fluctuation analysis.
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DOI：
10.1103/physreve.81.031101
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发表时间：
2010-03
期刊：
影响因子：
--
通讯作者：
Ivanov PCh
中科院分区：
文献类型：
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作者：
Ma QD;Bartsch RP;Bernaola-Galván P;Yoneyama M;Ivanov PCh
去趋势波动分析 (DFA) 是一种针对非平稳信号的经典波动分析的改进方法，其中嵌入的多项式趋势掩盖了波动的内在相关属性。为了更好地识别现实世界信号的内在相关特性，其中大量数据由于伪影而丢失或删除，我们研究了极端数据丢失如何影响远程幂律相关和反相关信号的缩放行为。我们引入了一种分段方法，通过从具有不同类型的远程相关性的平稳信号中随机删除数据段来生成代理信号。我们生成的代理信号由四个参数表征：(i) 原始相关信号 u(i) 的 DFA 缩放指数 α，(ii) 从 u(i) 中删除的数据的百分比 p，(iii) 删除（或剩余）数据段的平均长度 μ，以及（iv）删除（或剩余）数据段长度 l 的分布的函数形式 P(l)。我们发现，即使极端数据丢失高达 90%，正相关信号的全局标度指数实际上也保持不变。相反，即使只有一小部分数据丢失，反相关信号的全局缩放也会变为不相关行为。这些观察结果在现实世界信号的两个例子中得到了证实：人类步态和商品价格波动。我们进一步系统地研究缺失数据的替代信号的局部缩放行为，以揭示跨尺度的细微偏差。我们发现，对于反相关信号，即使 10% 的数据丢失也会导致大尺度局部缩放从原始反相关行为到不相关行为的显着单调偏差。相比之下，正相关信号显示，高达 65% 的数据丢失的局部缩放没有可观察到的变化，而对于较大百分比的数据丢失，局部缩放显示小尺度上高估的区域（具有较高的局部指数），其次是大尺度上的低估区域（具有较低的局部指数）。最后，我们研究平均长度、概率分布以及剩余数据段与删除段相比的百分比如何影响缩放。我们发现剩余段的平均长度μr是决定局部缩放指数与其原始值最大偏差的尺度的关键参数。有趣的是，出现最大偏差的尺度与 μr 遵循幂律关系。而数据丢失的百分比决定了偏差的程度。本文提出的结果有助于正确解释从具有极端数据丢失的信号中获得的缩放特性。
Detrended fluctuation analysis (DFA) is an improved method of classical fluctuation analysis for nonstationary signals where embedded polynomial trends mask the intrinsic correlation properties of the fluctuations. To better identify the intrinsic correlation properties of real-world signals where a large amount of data is missing or removed due to artifacts, we investigate how extreme data loss affects the scaling behavior of long-range power-law correlated and anticorrelated signals. We introduce a segmentation approach to generate surrogate signals by randomly removing data segments from stationary signals with different types of long-range correlations. The surrogate signals we generate are characterized by four parameters: (i) the DFA scaling exponent α of the original correlated signal u(i), (ii) the percentage p of the data removed from u(i), (iii) the average length μ of the removed (or remaining) data segments, and (iv) the functional form P(l) of the distribution of the length l of the removed (or remaining) data segments. We find that the global scaling exponent of positively correlated signals remains practically unchanged even for extreme data loss of up to 90%. In contrast, the global scaling of anticorrelated signals changes to uncorrelated behavior even when a very small fraction of the data is lost. These observations are confirmed on two examples of real-world signals: human gait and commodity price fluctuations. We further systematically study the local scaling behavior of surrogate signals with missing data to reveal subtle deviations across scales. We find that for anticorrelated signals even 10% of data loss leads to significant monotonic deviations in the local scaling at large scales from the original anticorrelated to uncorrelated behavior. In contrast, positively correlated signals show no observable changes in the local scaling for up to 65% of data loss, while for larger percentage of data loss, the local scaling shows overestimated regions (with higher local exponent) at small scales, followed by underestimated regions (with lower local exponent) at large scales. Finally, we investigate how the scaling is affected by the average length, probability distribution, and percentage of the remaining data segments in comparison to the removed segments. We find that the average length μr of the remaining segments is the key parameter which determines the scales at which the local scaling exponent has a maximum deviation from its original value. Interestingly, the scales where the maximum deviation occurs follow a power-law relationship with μr. Whereas the percentage of data loss determines the extent of the deviation. The results presented in this paper are useful to correctly interpret the scaling properties obtained from signals with extreme data loss.