Guarantees of augmented trace norm models in tensor recovery

  • Authors:
  • Ziqiang Shi;Jiqing Han;Tieran Zheng;Ji Li

  • Affiliations:
  • Fujitsu Research & Development Center, Beijing, China and Harbin Institute of Technology, Harbin, China;Harbin Institute of Technology, Harbin, China;Harbin Institute of Technology, Harbin, China;Beijing GuoDianTong Network Technology, Beijing, China

  • Venue:
  • IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
  • Year:
  • 2013

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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.