# Nonlinear Dimensionality Reduction with Diffusion Maps in Practice

arXiv: https://arxiv.org/abs/2601.20428 · HTML: https://mlsanity.com/paper/2601.20428/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 58 references that are in the map.
- First posted on arXiv 28 Jan 2026.

## Builds on (most cited first, 3 of 3)

- [Manifold learning: what, how, and why](https://mlsanity.com/paper/2311.03757/) (2023)
- [Diffusion Maps : Using the Semigroup Property for Parameter Tuning](https://mlsanity.com/paper/2203.02867/) (2022)
- [Wireless localization with diffusion maps](https://mlsanity.com/paper/1908.05216/) (2019)

## Abstract (arXiv)

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.