Learning non-geodesic submanifolds

Representation learning aims to transform data x into a lower-dimensional variable z designed to be more efficient for any downstream machine learning task, such as classification. In this project, you will tackle representation learning for manifold-valued data x, and specifically delve into non-geodesic submanifold learning with algorithms of curve fitting and variational autoencoders (rVAE) on manifolds. You will contribute to the open-source package Geomstats by implementing a representation learning module which will unify and contrast the aforementioned methods.

References

(*) Miolane et al. Geomstats: A Python Package for Riemannian Geometry in Machine Learning (JMLR 2020).

(*) Miolane, Holmes. Learning Weighted Submanifolds with Variational Autoencoders and Riemannian Variational Autoencoders (CVPR 2020).