Using extremal events to characterize noisy time series
Using extremal events to characterize noisy time series
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DOI：
10.1007/s00285-020-01471-4
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发表时间：
2020-02-01
影响因子：
1.9
通讯作者：
Gedeon, Tomas
中科院分区：
文献类型：
--
作者：
Berry, Eric;Cummins, Bree;Gedeon, Tomas
实验时间序列为潜在的动力系统提供了一个信息窗口，时间序列（或其导数）的极值时间包含了其结构的信息。然而，时间序列往往包含显著的测量误差。我们描述了一种方法来表征一个时间序列的任何假设水平的测量误差e的间隔序列，每一个都保证包含一个极值的任何函数，e逼近的时间序列。基于连续函数的合并树，我们定义了一个称为归一化分支分解的新对象，它允许我们计算任何级别e的区间。我们表明，对于单个时间序列，在这些区间上有一个定义良好的总阶，并且它可以自然地扩展到包含数据集的时间序列集合的偏阶。我们在两个应用中使用提取的区间的顺序。首先，描述单个数据集的偏序可用于针对切换模型输出的模式匹配（Cummins等人在SIAM J appll Dyn Syst 17(2):1589- 1616,2018），这允许拒绝网络模型。其次，不同数据集的偏序图距离的比较可以用来量化生物重复之间的相似性。
Experimental time series provide an informative window into the underlying dynamical system, and the timing of the extrema of a time series (or its derivative) contains information about its structure. However, the time series often contain significant measurement errors. We describe amethod for characterizing a time series for any assumed level of measurement error e by a sequence of intervals, each of which is guaranteed to contain an extremum for any function that e-approximates the time series. Based on the merge tree of a continuous function, we define a new object called the normalized branch decomposition, which allows us to compute intervals for any level e. We show that there is a well-defined total order on these intervals for a single time series, and that it is naturally extended to a partial order across a collection of time series comprising a dataset. We use the order of the extracted intervals in two applications. First, the partial order describing a single dataset can be used to pattern match against switching model output (Cummins et al. in SIAM J Appl Dyn Syst 17(2):1589-1616, 2018), which allows the rejection of a network model. Second, the comparison between graph distances of the partial orders of different datasets can be used to quantify similarity between biological replicates.