HaneWall / Manyfold.jl

Manifold Learning via Diffusion Maps in Julia

Manyfold

IN DEVELOPMENT, please issue bugs :)

Manifold Learning Package in Julia

Another manifold learning package in Julia. In this package we for now focus on nonlinear methods specifically the Diffusion Maps algorithm. Might add other nonlinear dimensionality reduction methods in future versions to justify "Many"fold.

Statement of Need:

1. missing / not working / wrong Diffusion Map algorithm in (no longer maintained?) ManifoldLearning.jl
2. first Julia Package to implement out of sample methods to map between Diffusion Map Coordinates and Ambient Space
3. provides lifting and restriction formalism to equation free methods with Diffusion Maps

Implemented Diffusion Map Methods

• Nyström extension for restriction for out of sample data
• k-nearest neighbor method for lifting (using NearestNeighbor.jl) from latent space to ambient space
• (Multi Scale) Geometric Harmonics for lifting and restriction

Acknowledgements

• package is inspired by ManifoldLearning.jl and Datafold (wonderful Python package)