Riemannian Perspective on Matrix Factorization
Optimization and Control
2021-02-02 v1 Machine Learning
Differential Geometry
Machine Learning
Abstract
We study the non-convex matrix factorization approach to matrix completion via Riemannian geometry. Based on an optimization formulation over a Grassmannian manifold, we characterize the landscape based on the notion of principal angles between subspaces. For the fully observed case, our results show that there is a region in which the cost is geodesically convex, and outside of which all critical points are strictly saddle. We empirically study the partially observed case based on our findings.
Cite
@article{arxiv.2102.00937,
title = {Riemannian Perspective on Matrix Factorization},
author = {Kwangjun Ahn and Felipe Suarez},
journal= {arXiv preprint arXiv:2102.00937},
year = {2021}
}
Comments
23 pages, 6 figures. Comments would be appreciated!