{"type":"ScholarlyArticle","title":"Beyond Low-rankness: Guaranteed Matrix Recovery via Modified Nuclear Norm","authors":[{"name":"Jiangjun Peng","slug":"jiangjun-peng","given":"Jiangjun","family":"Peng","affiliation":""},{"name":"Yisi Luo","slug":"yisi-luo","given":"Yisi","family":"Luo","affiliation":""},{"name":"Xiangyong Cao","slug":"xiangyong-cao","given":"Xiangyong","family":"Cao","affiliation":""},{"name":"Shuang Xu","slug":"shuang-xu","given":"Shuang","family":"Xu","affiliation":""},{"name":"Deyu Meng","slug":"deyu-meng","given":"Deyu","family":"Meng","affiliation":""}],"abstract":"The nuclear norm (NN) has been widely explored in matrix recovery problems, such as Robust PCA and matrix completion, leveraging the inherent global low-rank structure of the data. In this study, we introduce a new modified nuclear norm (MNN) framework, where the MNN family norms are defined by adopting suitable transformations and performing the NN on the transformed matrix. The MNN framework offers two main advantages: (1) it jointly captures both local information and global low-rankness without requiring trade-off parameter tuning; (2) under mild assumptions on the transformation, we provide theoretical recovery guarantees for both Robust PCA and MC tasks—an achievement not shared by existing methods that combine local and global information. Thanks to its general and flexible design, MNN can accommodate various proven transformations, enabling a unified and effective approach to structured low-rank recovery. Extensive experiments demonstrate the effectiveness of our method. Code and supplementary material are available at https://github.com/andrew-pengjj/modified_nuclear_norm.","doi":"10.24963/ijcai.2025/675","url":"https://ijcai.org/proceedings/2025/675","pdf":"https://ijcai.org/proceedings/2025/0675.pdf","markdown":"https://ijcai.org/proceedings/2025/675.md","bibtex":"https://ijcai.org/proceedings/2025/bibtex/675","volume":{"slug":"2025","title":"Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2025","url":"https://ijcai.org/proceedings/2025/","year":2025,"location":"Montreal, Canada","dates":"16-22 August 2025","editors":"James Kwok","isbn":"978-1-956792-06-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2025"},"section":"Machine Learning","track":"Main Track","number":675,"pages":{"first":6066,"last":6074},"keywords":["Machine Learning: ML: Matrix/tensor methods","Computer Vision: CV: Low-level Vision","Data Mining: DM: Theoretical foundations of data mining","Computer Vision: CV: Machine learning for vision"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}