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

09/12/2016

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by   Dohyung Park, et al.

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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 ∈R^m × n is represented as UV^, where U ∈R^m × r and V ∈R^n × 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.