{"type":"ScholarlyArticle","title":"Flexible Generalized Low-Rank Regularizer for Tensor RPCA","authors":[{"name":"Zhiyang Gong","slug":"zhiyang-gong","given":"Zhiyang","family":"Gong","affiliation":""},{"name":"Jie Yu","slug":"jie-yu","given":"Jie","family":"Yu","affiliation":""},{"name":"Yutao Hu","slug":"yutao-hu","given":"Yutao","family":"Hu","affiliation":""},{"name":"Yulong Wang","slug":"yulong-wang","given":"Yulong","family":"Wang","affiliation":""}],"abstract":"Tensor Robust Principal Component Analysis (TRPCA) has emerged as a powerful technique for low-rank tensor recovery.  To achieve better recovery performance, a variety of TNN (Tensor Nuclear Norm) based low-rank regularizers have been proposed case by case, lacking  a general and flexible framework. In this paper, we design a novel tensor low-rank regularization framework coined  FGTNN (Flexible Generalized Tensor Nuclear Norm). Equipped with FGTNN,  we develop the FGTRPCA (Flexible Generalized TRPCA) framework, which has two desirable properties. 1) Generalizability: Many existing TRPCA methods can be viewed as special cases of our framework; 2) Flexibility: Using FGTRPCA as a general platform, we derive a series of new TRPCA methods by tuning a continuous parameter to improve performance. In addition, we develop another novel smooth and low-rank regularizer coined t-FGJP and the resulting SFGTRPCA (Smooth FGTRPCA) method by leveraging the low-rankness and smoothness priors simultaneously. Experimental results on various tensor denoising and recovery tasks demonstrate the superiority of our methods.","doi":"10.24963/ijcai.2025/583","url":"https://ijcai.org/proceedings/2025/583","pdf":"https://ijcai.org/proceedings/2025/0583.pdf","markdown":"https://ijcai.org/proceedings/2025/583.md","bibtex":"https://ijcai.org/proceedings/2025/bibtex/583","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":583,"pages":{"first":5235,"last":5243},"keywords":["Machine Learning: ML: Robustness","Machine Learning: ML: Matrix/tensor methods"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}