Guarantees of Augmented Trace Norm Models in Tensor RecoveryOpen Website

2013 (modified: 16 Jul 2019)IJCAI 2013Readers: Everyone
Abstract: This paper studies the recovery guarantees of the models of minimizing ||χ||* + 1/2α||χ||F2 where χ is a tensor and ||χ||* and ||χ||F are the trace and Frobenius norm of respectively. We show that they can efficiently recover low-rank tensors. In particular, they enjoy exact guarantees similar to those known for minimizing ||χ||* under the conditions on the sensing operator such as its null-space property, restricted isometry property, or spherical section property. To recover a low-rank tensor χ0, minimizing ||χ||* + 1/2α||χ||F2 returns the same solution as minimizing ||χ||* almost whenever α ≥ 10 max i ||X(i)0||2.
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