Riemannian Perspective on Matrix Factorization
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.
PDF AbstractTasks
Datasets
Add Datasets
introduced or used in this paper
Results from the Paper
Submit
results from this paper
to get state-of-the-art GitHub badges and help the
community compare results to other papers.
Methods
No methods listed for this paper. Add
relevant methods here
