Diffusion Maps meet Nystr\"om

TL;DR

This paper combines diffusion maps with the Nyström method to significantly reduce computational costs, enabling efficient analysis of large-scale nonlinear dynamical systems.

Contribution

It introduces a novel integration of diffusion maps and Nyström method, achieving faster computation of diffusion components for large datasets.

Findings

Speedup of 2-4 times in diffusion map computation

Effective approximation of dominant diffusion components

Enhanced scalability for long time-series data

Abstract

Diffusion maps are an emerging data-driven technique for non-linear dimensionality reduction, which are especially useful for the analysis of coherent structures and nonlinear embeddings of dynamical systems. However, the computational complexity of the diffusion maps algorithm scales with the number of observations. Thus, long time-series data presents a significant challenge for fast and efficient embedding. We propose integrating the Nystr\"om method with diffusion maps in order to ease the computational demand. We achieve a speedup of roughly two to four times when approximating the dominant diffusion map components.