Diffusion Geometry

diffusion_geometry.py

Video discussing pointing to text 'Diffusion Geometry' (May 2024, 49 pages) 
by Iolo Jones (Durham University)

https://www.youtube.com/watch?v=f2GJG7vMSZI

#### Links
* Paper:
https://arxiv.org/abs/2405.10858
https://arxiv.org/pdf/2405.10858

* Github
https://github.com/Iolo-Jones/DiffusionGeometry

* The author on x:
https://x.com/iolo_jones/

* The Wikipeda pages I browsed in the video
https://en.wikipedia.org/wiki/Carr%C3%A9_du_champ_operator

see also
https://en.wikipedia.org/wiki/Laplace%E2%80%93Beltrami_operator
https://en.wikipedia.org/wiki/Diffusion_equation

#### Table of contents
1 introduction 1
2 Markov Diffusion Operators and Markov Triples 3
3 Theory of Diffusion Geometry 6
4 Computing Diffusion Geometry from Data 20
5 Computational Geometry and Topology, Machine Learning, and Statistics 23
6 Computational Complexity 29
7 Comparison with Related Work 30
8 Conclusions 31
9 Appendix A: Proofs 32
10 Appendix B: Implementation Details 43

#### Notes
g => Γ
Related operators
L(μ) = 0
P_t(μ) = μ