---
title: "Guarantees of Augmented Trace Norm Models in Tensor Recovery"
authors:
  - "Ziqiang Shi"
  - "Jiqing Han"
  - "Tieran Zheng"
  - "Ji Li"
doi: ""
url: "https://ijcai.org/proceedings/2013/248"
pdf: "https://ijcai.org/proceedings/2013/0248.pdf"
venue: "Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence"
year: 2013
pages: "1670-1675"
track: ""
keywords:
---

# Guarantees of Augmented Trace Norm Models in Tensor Recovery

Ziqiang Shi, Jiqing Han, Tieran Zheng, Ji Li

*Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence*, pages 1670-1675.

## Abstract

This paper studies the recovery guarantees of the models of minimizing ||X||∗ + 1/2a ||X||2F where X is a tensor and ||X||∗ and ||X||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 ||X||∗ 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 X0, minimizing ||X||∗ + 1/2a ||X||2F returns the same solution as minimizing ||X||∗ almost whenever α ≥ 10max ||X0(i)||2.