This work presents a novel framework for time series analysis using entropic measures based on the kernel density estimate (KDE) of the time series' Takens' embeddings. Using this framework we introduce two distinct analytical tools: (1) a multi-scale KDE entropy metric, denoted as $\Delta\text{KE}$, which quantifies the evolution of time series complexity across different scales by measuring certain entropy changes, and (2) a sliding baseline method that employs the Kullback-Leibler (KL) divergence to detect changes in time series dynamics through changes in KDEs. The $\Delta{\rm KE}$ metric offers insights into the information content and ``unfolding'' properties of the time series' embedding related to dynamical systems, while the KL divergence-based approach provides a noise and outlier robust approach for identifying time series change points (injections in RF signals, e.g.). We demonstrate the versatility and effectiveness of these tools through a set of experiments encompassing diverse domains. In the space of radio frequency (RF) signal processing, we achieve accurate detection of signal injections under varying noise and interference conditions. Furthermore, we apply our methodology to electrocardiography (ECG) data, successfully identifying instances of ventricular fibrillation with high accuracy. Finally, we demonstrate the potential of our tools for dynamic state detection by accurately identifying chaotic regimes within an intermittent signal. These results show the broad applicability of our framework for extracting meaningful insights from complex time series data across various scientific disciplines.

翻译：本研究提出了一种新颖的时间序列分析框架，该框架利用基于时间序列Takens嵌入的核密度估计（KDE）的熵测度。通过此框架，我们引入了两种不同的分析工具：（1）一种多尺度KDE熵度量，记为$\Delta\text{KE}$，它通过测量特定的熵变化来量化时间序列复杂度在不同尺度上的演变；（2）一种滑动基线方法，该方法利用Kullback-Leibler（KL）散度通过KDE的变化来检测时间序列动力学的变化。$\Delta{\rm KE}$度量揭示了与动力系统相关的时间序列嵌入的信息内容和“展开”特性，而基于KL散度的方法则提供了一种对噪声和异常值鲁棒的、用于识别时间序列变化点（例如，RF信号中的注入）的方法。我们通过一系列涵盖不同领域的实验证明了这些工具的通用性和有效性。在射频（RF）信号处理领域，我们在变化的噪声和干扰条件下实现了信号注入的精确检测。此外，我们将我们的方法应用于心电图（ECG）数据，成功高精度地识别了心室颤动的实例。最后，我们通过精确识别间歇信号内的混沌状态，展示了我们的工具在动态状态检测方面的潜力。这些结果表明，我们的框架在从跨不同科学学科的复杂时间序列数据中提取有意义见解方面具有广泛的适用性。