Entropic Analysis of Time Series through Kernel Density Estimation

2025-03-24

AI Summary

This paper addresses the challenges of modeling multiscale complexity evolution in time series and robustly detecting dynamic change points. Methodologically, it proposes an entropy analysis framework integrating Takens’ embedding with kernel density estimation (KDE). First, it introduces a multiscale KDE entropy variation metric, ΔKE, which quantifies the scale-dependent information expansion within the reconstructed phase space—a novel characterization. Second, it designs a change-point detection algorithm based on sliding-baseline KL divergence, markedly enhancing noise resilience and robustness to outliers. Empirical evaluation demonstrates high-precision identification of injected events in RF signals, accurate ventricular fibrillation detection in ECG data, and successful recognition of intermittent chaotic states. These results validate the framework’s broad applicability and effectiveness across domains including wireless communications, clinical diagnostics, and nonlinear dynamical systems.

Technology Category

• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Machine Learning: Kernel Methods
• Intelligent Robots: State Estimation

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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 $Δ ext{KE}$, 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 $Δ{ m KE}$ 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.

Problem

• Develops multi-scale entropy metric for time series complexity analysis
• Introduces Kullback-Leibler divergence method for change point detection
• Applies framework to RF signals and ECG data for anomaly detection

Innovation

• Multi-scale KDE entropy for complexity evolution
• KL divergence for robust change point detection
• Takens' embeddings with kernel density estimation