Analyzing high-dimensional time-series data using kernel transfer operator eigenfunctions

TL;DR

This paper introduces a method using kernel transfer operator eigenfunctions combined with gradient optimization to identify persistent patterns in high-dimensional time-series data, demonstrated through video and fluid flow examples.

Contribution

It presents a novel approach that leverages kernel transfer operators and eigenfunctions for analyzing complex time-series data, enhancing pattern detection capabilities.

Findings

Effective detection of long-lived coherent structures

Application to high-dimensional video and fluid flow data

Improved understanding of dynamic patterns

Abstract

Kernel transfer operators, which can be regarded as approximations of transfer operators such as the Perron-Frobenius or Koopman operator in reproducing kernel Hilbert spaces, are defined in terms of covariance and cross-covariance operators and have been shown to be closely related to the conditional mean embedding framework developed by the machine learning community. The goal of this paper is to show how the dominant eigenfunctions of these operators in combination with gradient-based optimization techniques can be used to detect long-lived coherent patterns in high-dimensional time-series data. The results will be illustrated using video data and a fluid flow example.