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arXiv · 2601.20428

Nonlinear Dimensionality Reduction with Diffusion Maps in Practice

Sönke Beier·Paula Pirker-Díaz·Friedrich Pagenkopf·Karoline Wiesner
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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.

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Sönke Beier, Paula Pirker-Díaz, Friedrich Pagenkopf, Karoline Wiesner. 2026-01-28. Nonlinear Dimensionality Reduction with Diffusion Maps in Practice. https://arxiv.org/abs/2601.20428

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