# Dictionary-based Manifold Learning

arXiv: https://arxiv.org/abs/2302.00263 · HTML: https://mlsanity.com/paper/2302.00263/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 31 references that are in the map.
- First posted on arXiv 1 Feb 2023.

## Builds on (most cited first, 2 of 2)

- [Graph Dynamical Networks for Unsupervised Learning of Atomic Scale Dynamics in Materials](https://mlsanity.com/paper/1902.06836/) (2019)
- [Improved graph Laplacian via geometric self-consistency](https://mlsanity.com/paper/1406.0118/) (2014)

## Abstract (arXiv)

We propose a paradigm for interpretable Manifold Learning for scientific data analysis, whereby we parametrize a manifold with d smooth functions from a scientist-provided dictionary of meaningful, domain-related functions. When such a parametrization exists, we provide an algorithm for finding it based on sparse non-linear regression in the manifold tangent bundle, bypassing more standard manifold learning algorithms. We also discuss conditions for the existence of such parameterizations in function space and for successful recovery from finite samples. We demonstrate our method with experimental results from a real scientific domain.