论文标题
极端事件图：用于分析嘈杂时间序列数据的（稳定）工具
Extremal Event Graphs: A (Stable) Tool for Analyzing Noisy Time Series Data
论文作者
论文摘要
实验时间序列中的本地最大值和最小值或极端事件可以用作表征数据的粗略摘要。然而，记录实验测量中的离散抽样表明实验过程中极值的真实时机不确定性。反过来，这在时间序列中的极端计时顺序中给出了不确定性。由基因组时间序列和生物网络分析中的应用激励，我们使用持久同源性的技术构建了称为极端事件DAG的加权定向无环图（DAG），该技术对测量噪声是可靠的。此外，我们根据字符串之间的编辑距离定义了极端事件DAG之间的距离。我们证明了几个属性，包括相对于成对$ l _ {\ infty} $在时间序列数据中函数之间的距离$ l _ {\ infty} $的局部稳定性。最后，我们提供有关极端事件DAG构造和比较的算法，公开免费软件和实施。
Local maxima and minima, or extremal events, in experimental time series can be used as a coarse summary to characterize data. However, the discrete sampling in recording experimental measurements suggests uncertainty on the true timing of extrema during the experiment. This in turn gives uncertainty in the timing order of extrema within the time series. Motivated by applications in genomic time series and biological network analysis, we construct a weighted directed acyclic graph (DAG) called an extremal event DAG using techniques from persistent homology that is robust to measurement noise. Furthermore, we define a distance between extremal event DAGs based on the edit distance between strings. We prove several properties including local stability for the extremal event DAG distance with respect to pairwise $L_{\infty}$ distances between functions in the time series data. Lastly, we provide algorithms, publicly free software, and implementations on extremal event DAG construction and comparison.
