Manifold Learning
What's Manifold Learning? Manifold Learning is merely using the geometric properties of the data in high dimensions to implement the following things:
- Clustering: Find groups of similar points. Given
, build a function . Two "close" points should be in the same cluster. - Dimensionality Reduction: Project points in a lower dimensional
space while preserving structure. Given
in , build a function , where . "Closeness" should be preserved. - Semi-Supervised, Supervised: Given labelled and unlabeled points,
build a labeling function. Given
, build . Two "close" points should have the same label.
Manifold Learning assumes that the observed data lie on a low-dimensional manifold embedded in a higher-diemnsional space. This is known as manifold assumption.
References
[1] https://towardsdatascience.com/manifold-learning-the-theory-behind-it-c34299748fec
[2] @phdthesis{melas2020mathematical, title={The Mathematical Foundations of Manifold Learning}, author={Melas-Kyriazi, Luke}, year={2020}, school={Harvard University Cambridge, Massachusetts} }