Ferré John, Rokem Ariel, Buffalo Elizabeth A, Kutz J Nathan, Fairhall Adrienne
Physics Department, University of Washington, Seattle, Washington 98195, USA.
Psychology Department and eScience Institute, University of Washington, Seattle, Washington 98195, USA.
bioRxiv. 2023 Aug 13:2023.08.08.552333. doi: 10.1101/2023.08.08.552333.
Many physical processes display complex high-dimensional time-varying behavior, from global weather patterns to brain activity. An outstanding challenge is to express high dimensional data in terms of a dynamical model that reveals their spatiotemporal structure. Dynamic Mode Decomposition is a means to achieve this goal, allowing the identification of key spatiotemporal modes through the diagonalization of a finite dimensional approximation of the Koopman operator. However, DMD methods apply best to time-translationally invariant or stationary data, while in many typical cases, dynamics vary across time and conditions. To capture this temporal evolution, we developed a method, Non-Stationary Dynamic Mode Decomposition (NS-DMD), that generalizes DMD by fitting global modulations of drifting spatiotemporal modes. This method accurately predicts the temporal evolution of modes in simulations and recovers previously known results from simpler methods. To demonstrate its properties, the method is applied to multi-channel recordings from an awake behaving non-human primate performing a cognitive task.
许多物理过程都呈现出复杂的高维时变行为，从全球天气模式到大脑活动皆是如此。一个突出的挑战是，要依据能揭示其时空结构的动力学模型来表达高维数据。动态模式分解是实现这一目标的一种手段，它通过对柯普曼算子的有限维近似进行对角化，来识别关键的时空模式。然而，动态模式分解方法最适用于时间平移不变或平稳的数据，而在许多典型情况下，动力学随时间和条件而变化。为了捕捉这种时间演化，我们开发了一种方法，即非平稳动态模式分解（NS-DMD），它通过拟合漂移时空模式的全局调制来推广动态模式分解。该方法在模拟中能准确预测模式的时间演化，并从更简单的方法中恢复先前已知的结果。为了展示其特性，该方法被应用于一只正在执行认知任务的清醒行为非人类灵长类动物的多通道记录。
