# Functional Diffusion Maps

arXiv: https://arxiv.org/abs/2304.14378 · HTML: https://mlsanity.com/paper/2304.14378/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 51 references that are in the map.
- First posted on arXiv 27 Apr 2023.

## Builds on (most cited first, 5 of 5)

- [Learning by Unsupervised Nonlinear Diffusion](https://mlsanity.com/paper/1810.06702/) (2018)
- [scikit-fda: A Python Package for Functional Data Analysis](https://mlsanity.com/paper/2211.02566/) (2022)
- [Benchmarking time series classification -- Functional data vs machine learning approaches](https://mlsanity.com/paper/1911.07511/) (2019)
- [Unsupervised Functional Data Analysis via Nonlinear Dimension Reduction](https://mlsanity.com/paper/2012.11987/) (2020)
- [Variable selection in functional data classification: a maxima-hunting proposal](https://mlsanity.com/paper/1309.6697/) (2013)

## Built on by (most cited first, 1 of 1)

- [Deep Diffusion Maps](https://mlsanity.com/paper/2505.06087/) (2025)

## Abstract (arXiv)

Nowadays many real-world datasets can be considered as functional, in the sense that the processes which generate them are continuous. A fundamental property of this type of data is that in theory they belong to an infinite-dimensional space. Although in practice we usually receive finite observations, they are still high-dimensional and hence dimensionality reduction methods are crucial. In this vein, the main state-of-the-art method for functional data analysis is Functional PCA. Nevertheless, this classic technique assumes that the data lie in a linear manifold, and hence it could have problems when this hypothesis is not fulfilled. In this research, attention has been placed on a non-linear manifold learning method: Diffusion Maps. The article explains how to extend this multivariate method to functional data and compares its behavior against Functional PCA over different simulated and real examples.