ANAPT：用于持久性保持的加性噪声分析
ANAPT: Additive Noise Analysis for Persistence Thresholding
摘要：
本文提出了一种新的加性噪声持久性分析方法（ANAPT），该方法基于噪声分布的持久性统计分析，分离出时间序列的子水平集持久性图中的重要特征。具体来说，我们考虑一个加性噪声模型，并利用统计分析提供一个噪音截止或置信区间的持久性图所观察到的时间序列。这种分析是针对几种常见的噪声模型进行的，包括高斯分布、均匀分布、指数分布和瑞利分布。ANAPT计算效率高，不需要任何信号预滤波，适用范围广，并且有开源软件可用。我们演示了数值模拟的例子和实验数据集的功能ANAPT。此外，我们提供了一个有效的$Θ(n\log(n))$算法计算零维子水平集持久性的同源。
英文摘要：
We introduce a novel method for Additive Noise Analysis for Persistence Thresholding (ANAPT) which separates significant features in the sublevel set persistence diagram of a time series based on a statistics analysis of the persistence of a noise distribution. Specifically, we consider an additive noise model and leverage the statistical analysis to provide a noise cutoff or confidence interval in the persistence diagram for the observed time series. This analysis is done for several common noise models including Gaussian, uniform, exponential and Rayleigh distributions. ANAPT is computationally efficient, does not require any signal pre-filtering, is widely applicable, and has open-source software available. We demonstrate the functionality ANAPT with both numerically simulated examples and an experimental data set. Additionally, we provide an efficient $Θ(n\log(n))$ algorithm for calculating the zero-dimensional sublevel set persistence homology.
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