Riemannian Perspective on Matrix Factorization

Kwangjun Ahn; Felipe Suarez

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arXiv · 2102.00937

Riemannian Perspective on Matrix Factorization

Kwangjun Ahn·Felipe Suarez

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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.

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Kwangjun Ahn, Felipe Suarez. 2021-02-01. Riemannian Perspective on Matrix Factorization. https://arxiv.org/abs/2102.00937

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