This article presents a novel, nonlinear, data-driven signal processing method, which can help neuroscience researchers visualize and understand complex dynamical patterns in both time and space. Specifically, we present applications of a Koopman operator approach for eigendecomposition of electrophysiological signals into orthogonal, coherent components and examine their associated spatiotemporal dynamics. This approach thus provides enhanced capabilities over conventional computational neuroscience tools restricted to analyzing signals in either the time or space domains. This is achieved via machine learning and kernel methods for data-driven approximation of skew-product dynamical systems. The approximations successfully converge to theoretical values in the limit of long embedding windows. First, we describe the method, then using electrocorticographic (ECoG) data from a mismatch negativity experiment, we extract time-separable frequencies without bandpass filtering or prior selection of wavelet features. Finally, we discuss in detail two of the extracted components, Beta (∼\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \sim $\end{document} 13 Hz) and high Gamma (∼\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \sim $\end{document} 50 Hz) frequencies, and explore the spatiotemporal dynamics of high- and low- frequency components.

中文翻译：

---

用于计算神经科学的数据驱动的 Koopman 算子方法

本文提出了一种新颖的、非线性的、数据驱动的信号处理方法，它可以帮助神经科学研究人员在时间和空间上可视化和理解复杂的动态模式。具体来说，我们介绍了 Koopman 算子方法将电生理信号特征分解为正交、相干分量的应用，并检查它们相关的时空动力学。因此，与仅限于分析时域或空间域中的信号的传统计算神经科学工具相比，这种方法提供了增强的功能。这是通过机器学习和内核方法实现的，用于斜积动态系统的数据驱动逼近。在长嵌入窗口的限制下，近似值成功收敛到理论值。首先，我们描述方法，然后使用来自失配负性实验的脑电图 (ECoG) 数据，我们提取时间可分离频率，无需带通滤波或事先选择小波特征。最后，我们详细讨论提取的两个组件 Beta (∼\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage {mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \sim $\end{document} 13 Hz) 和高伽玛 (∼\documentclass[12pt]{minimal} \usepackage {amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \ sim $\end{document} 50 Hz) 频率，