Visualizing High Dimensional Dynamical Processes
This work addresses visualization challenges in multivariate time series analysis, particularly for applications like EEG sleep stage monitoring, but appears incremental as it builds on existing manifold learning techniques.
The authors tackled the problem of visualizing high-dimensional dynamical processes by introducing DIG, a method that extracts an information geometry from a diffusion framework, and demonstrated its application to EEG data for visualizing sleep stages.
Manifold learning techniques for dynamical systems and time series have shown their utility for a broad spectrum of applications in recent years. While these methods are effective at learning a low-dimensional representation, they are often insufficient for visualizing the global and local structure of the data. In this paper, we present DIG (Dynamical Information Geometry), a visualization method for multivariate time series data that extracts an information geometry from a diffusion framework. Specifically, we implement a novel group of distances in the context of diffusion operators, which may be useful to reveal structure in the data that may not be accessible by the commonly used diffusion distances. Finally, we present a case study applying our visualization tool to EEG data to visualize sleep stages.