{"type":"ScholarlyArticle","title":"Joint Capped Norms Minimization for Robust Matrix Recovery","authors":[{"name":"Feiping Nie","slug":"feiping-nie","given":"Feiping","family":"Nie","affiliation":"School of Computer Science and Center for OPTical IMagery Analysis and Learning (OPTIMAL) , Northwestern Polytechnical University , Xian 710072 , Shaanxi , P. R. China."},{"name":"Zhouyuan Huo","slug":"zhouyuan-huo","given":"Zhouyuan","family":"Huo","affiliation":"Computer Science and Engineering , University of Texas at Arlington , USA."},{"name":"Heng Huang","slug":"heng-huang","given":"Heng","family":"Huang","affiliation":"Computer Science and Engineering , University of Texas at Arlington , USA."}],"abstract":"The low-rank matrix recovery is an important machine learning research topic with various scientific applications. Most existing low-rank matrix recovery methods relax the rank minimization problem via the trace norm minimization. However, such a relaxation makes the solution seriously deviate from the original one. Meanwhile, most matrix recovery methods minimize the squared prediction errors on the observed entries, which is sensitive to outliers. In this paper, we propose a new robust matrix recovery model to address the above two challenges. The joint capped trace norm and capped $\\ell_1$-norm are used to tightly approximate the rank minimization and enhance the robustness to outliers. The evaluation experiments are performed on both synthetic data and real world applications in collaborative filtering and social network link prediction. All empirical results show our new method outperforms the existing matrix recovery methods.","doi":"10.24963/ijcai.2017/356","url":"https://ijcai.org/proceedings/2017/356","pdf":"https://ijcai.org/proceedings/2017/0356.pdf","markdown":"https://ijcai.org/proceedings/2017/356.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/356","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra, IIIA-CSIC","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Machine Learning A-R","track":"Main track","number":356,"pages":{"first":2557,"last":2563},"keywords":["Machine Learning: Data Mining","Machine Learning: Learning Preferences or Rankings"],"videos":[],"references":[{"position":1,"raw":"[Abernethy et al., 2009] J. 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