{"type":"ScholarlyArticle","title":"Nonconvex Relaxation Approaches to Robust Matrix Recovery","authors":[{"name":"Shusen Wang","slug":"shusen-wang","given":"Shusen","family":"Wang","affiliation":""},{"name":"Dehua Liu","slug":"dehua-liu","given":"Dehua","family":"Liu","affiliation":""},{"name":"Zhihua Zhang","slug":"zhihua-zhang","given":"Zhihua","family":"Zhang","affiliation":""}],"abstract":"Motivated by the recent developments of nonconvex penalties in sparsity modeling, we propose a nonconvex optimization model for handing the low-rank matrix recovery problem. Different from the famous robust principal component analysis (RPCA), we suggest recovering low-rank and sparse matrices via a nonconvex loss function and a nonconvex penalty. The advantage of the nonconvex approach lies in its stronger robustness. To solve the model, we devise a majorization-minimization augmented Lagrange multiplier (MM-ALM) algorithm which finds the local optimal solutions of the proposed nonconvex model. We also provide an efficient strategy to speedup MM-ALM, which makes the running time comparable with the state-of-the-art algorithm of solving RPCA. Finally, empirical results demonstrate the superiority of our nonconvex approach over RPCA in terms of matrix recovery accuracy.","doi":null,"url":"https://ijcai.org/proceedings/2013/261","pdf":"https://ijcai.org/proceedings/2013/0261.pdf","markdown":"https://ijcai.org/proceedings/2013/261.md","bibtex":"https://ijcai.org/proceedings/2013/bibtex/261","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":261,"pages":{"first":1764,"last":1769},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}