论文标题
相关噪声对基于持久性动态状态检测方法性能的影响
Effects of Correlated Noise on the Performance of Persistence Based Dynamic State Detection Methods
论文作者
论文摘要
表征动态系统状态的能力一直是时间序列分析社区中的一项相关任务。传统措施（例如Lyapunov指数）通常很难从嘈杂的数据中恢复，尤其是在系统的维度尚不清楚的情况下。最新的基于二进制和网络的测试方法为未知的确定性系统带来了有希望的结果，但是注入周期性信号的噪声会导致误报。最近，我们展示了使用持续同源性作为实现没有已知模型的系统的动态状态检测的工具的优势，并显示了其对白色高斯噪声的鲁棒性。在这项工作中，我们探讨了基于持久性的方法对彩色噪声影响的鲁棒性，并表明表格$ 1/f^α$的彩色噪声过程导致以$α<0 $ $α<0 $的噪声比下的较低信号与噪声比的假阳性诊断。
The ability to characterize the state of dynamic systems has been a pertinent task in the time series analysis community. Traditional measures such as Lyapunov exponents are often times difficult to recover from noisy data, especially if the dimensionality of the system is not known. More recent binary and network based testing methods have delivered promising results for unknown deterministic systems, however noise injected into a periodic signal leads to false positives. Recently, we showed the advantage of using persistent homology as a tool for achieving dynamic state detection for systems with no known model and showed its robustness to white Gaussian noise. In this work, we explore the robustness of the persistence based methods to the influence of colored noise and show that colored noise processes of the form $1/f^α$ lead to false positive diagnostic at lower signal to noise ratios for $α<0$.
