Non-square matrix sensing without spurious local minima via the Burer-Monteiro approach

Abstract

We consider the non-square matrix sensing problem, under restricted isometry property (RIP) assumptions. We focus on the non-convex formulation, where any rank-$r$ matrix $X\in {\mathbb{R}}^{m\times n}$ is represented as $U{V}^{\top }$, where $U\in {\mathbb{R}}^{m\times r}$ and $V\in {\mathbb{R}}^{n\times r}$. In this paper, we complement recent findings on the non-convex geometry of the analogous PSD setting [5], and show that matrix factorization does not introduce any spurious local minima, under RIP.

14 pages, no figures

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