用于时空动力学分解的相位对准谱滤波
Phase-Aligned Spectral Filtering for Decomposing Spatiotemporal Dynamics
摘要：
时空动力学是从气候学、计算机视觉到神经科学的广泛应用的核心。从一个高维向量的空间位置的时间观测，我们试图通过数据同化和建模来获得有关这种动态的知识。它是假设所观察到的时空数据表示叠加的低秩平滑振荡和运动，从一个生成的动态系统，与高阶随机噪声混合。从噪声中分离信号对于我们可视化、建模和理解这些低秩动态系统是至关重要的。通常情况下，这种低秩动态系统具有多个独立的组件，对应于所研究系统的不同趋势或功能。在本文中，我们提出了一种新的过滤框架，用于识别嵌入在高维时空系统中的低秩动态及其组件。它是基于在频域中的结构分解和相位对齐的建设的方法。在我们的模拟例子和实际数据的应用中，我们说明了所提出的方法是能够分离和识别有意义的低秩运动，而现有的方法失败。
英文摘要：
Spatiotemporal dynamics is central to a wide range of applications from climatology, computer vision to neural sciences. From temporal observations taken on a high-dimensional vector of spatial locations, we seek to derive knowledge about such dynamics via data assimilation and modeling. It is assumed that the observed spatiotemporal data represent superimposed lower-rank smooth oscillations and movements from a generative dynamic system, mixed with higher-rank random noises. Separating the signals from noises is essential for us to visualize, model and understand these lower-rank dynamic systems. It is also often the case that such a lower-rank dynamic system have multiple independent components, corresponding to different trends or functionalities of the system under study. In this paper, we present a novel filtering framework for identifying lower-rank dynamics and its components embedded in a high dimensional spatiotemporal system. It is based on an approach of structural decomposition and phase-aligned construction in the frequency domain. In both our simulated examples and real data applications, we illustrate that the proposed method is able to separate and identify meaningful lower-rank movements, while existing methods fail.
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