Nonlinear Dimensionality Reduction with Diffusion Maps in Practice
Machine Learning
2026-01-29 v1 Applications
Abstract
Diffusion Map is a spectral dimensionality reduction technique which is able to uncover nonlinear submanifolds in high-dimensional data. And, it is increasingly applied across a wide range of scientific disciplines, such as biology, engineering, and social sciences. But data preprocessing, parameter settings and component selection have a significant influence on the resulting manifold, something which has not been comprehensively discussed in the literature so far. We provide a practice oriented review of the Diffusion Map technique, illustrate pitfalls and showcase a recently introduced technique for identifying the most relevant components. Our results show that the first components are not necessarily the most relevant ones.
Cite
@article{arxiv.2601.20428,
title = {Nonlinear Dimensionality Reduction with Diffusion Maps in Practice},
author = {Sönke Beier and Paula Pirker-Díaz and Friedrich Pagenkopf and Karoline Wiesner},
journal= {arXiv preprint arXiv:2601.20428},
year = {2026}
}