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• W3111234197 abstract "The restricted isometry property (RIP) is a well-known condition that guarantees the absence of spurious local minima in low-rank matrix recovery problems with linear measurements. In this paper, we introduce a novel property named bound difference property (BDP) to study low-rank matrix recovery problems with nonlinear measurements. Using RIP and BDP jointly, we first focus on the rank-1 matrix recovery problem, for which we propose a new criterion to certify the nonexistence of spurious local minima over the entire space. We then analyze the general case with an arbitrary rank and derive a condition to rule out the possibility of having a spurious solution in a ball around the true solution. The developed conditions lead to much stronger theoretical guarantees than the existing bounds on RIP." @default.
• W3111234197 created "2020-12-21" @default.
• W3111234197 creator A5042580848 @default.
• W3111234197 creator A5057565845 @default.
• W3111234197 date "2020-10-09" @default.
• W3111234197 modified "2023-09-27" @default.
• W3111234197 title "Global and Local Analyses of Nonlinear Low-Rank Matrix Recovery Problems." @default.
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• W3111234197 hasPublicationYear "2020" @default.
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