{"type":"ScholarlyArticle","title":"Guarantees of Augmented Trace Norm Models in Tensor Recovery","authors":[{"name":"Ziqiang Shi","slug":"ziqiang-shi","given":"Ziqiang","family":"Shi","affiliation":""},{"name":"Jiqing Han","slug":"jiqing-han","given":"Jiqing","family":"Han","affiliation":""},{"name":"Tieran Zheng","slug":"tieran-zheng","given":"Tieran","family":"Zheng","affiliation":""},{"name":"Ji Li","slug":"ji-li","given":"Ji","family":"Li","affiliation":""}],"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.","doi":null,"url":"https://ijcai.org/proceedings/2013/248","pdf":"https://ijcai.org/proceedings/2013/0248.pdf","markdown":"https://ijcai.org/proceedings/2013/248.md","bibtex":"https://ijcai.org/proceedings/2013/bibtex/248","volume":{"slug":"2013","title":"Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2013","url":"https://ijcai.org/proceedings/2013/","year":2013,"location":"Beijing, China","dates":"3–9 August 2013","editors":"Francesca Rossi","isbn":"978-1-57735-633-2","publisher":"AAAI Press / International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":248,"pages":{"first":1670,"last":1675},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}