# Visualizing High Dimensional Dynamical Processes

## TL;DR

This paper introduces DIG, a visualization method for multivariate time series that uses information geometry derived from diffusion operators to reveal complex data structures, demonstrated on EEG sleep stage data.

## Contribution

The paper presents a novel visualization technique, DIG, which employs a new group of diffusion-based distances to better reveal data structure in high-dimensional dynamical processes.

## Key findings

- DIG effectively visualizes sleep stages in EEG data.
- New diffusion-based distances reveal structures not seen with traditional methods.
- Method enhances understanding of high-dimensional dynamical systems.

## Abstract

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.