论文标题
ANAPT：持久性阈值的添加噪声分析
ANAPT: Additive Noise Analysis for Persistence Thresholding
论文作者
论文摘要
我们介绍了一种用于持久性阈值（ANAPT）的添加噪声分析的新方法，该方法基于对噪声分布持久性的统计分析，将时间序列的持久性图分开。具体而言，我们考虑一个加性噪声模型，并利用统计分析以在观察到的时间序列的持久图中提供噪声截断或置信区间。该分析是针对几种常见的噪声模型进行的，包括高斯，统一，指数和瑞利分布。 ANAPT在计算上是有效的，不需要任何信号预过滤，广泛适用，并且具有开源软件。我们通过数值模拟的示例和实验数据集演示了功能ANAPT。此外，我们提供有效的$θ（n \ log（n））$算法，用于计算零维的sublevel set持久性同源性。
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.
