{"type":"ScholarlyArticle","title":"Atomic Recovery Property for Multi-view Subspace-Preserving Recovery","authors":[{"name":"Yulong Wang","slug":"yulong-wang","given":"Yulong","family":"Wang","affiliation":"College of Informatics , Huazhong Agricultural University , China; Engineering Research Center of Intelligent Technology for Agriculture , Ministry of Education , China; Key Laboratory of Smart Farming Technology for Agricultural Animals , Ministry of Agriculture and Rural Affairs , China"}],"abstract":"As the theoretical underpinnings for subspace clustering and classification, subspace-preserving recovery has attracted intensive attention in recent years. However, previous theoretical advances for subspace-preserving recovery only focus on the single-view data and most of them are based on conditions that are only sufficient. In this paper, we propose a necessary and sufficient condition referred to as Atomic Recovery Property (ARP) for multi-view subspace-preserving recovery. To this end, we generalize the atomic norm from single-view data to multi-view data and define the Multi-view Atomic Norm (MAN). Our another contribution is to provide a geometrically more interpretable characterization of ARP with respect to the unit ball of MAN. Based on the proposed multi-view subspace-preserving recovery theory, we also derive novel theoretical results for multi-view subspace clustering and classification, respectively.","doi":"10.24963/ijcai.2024/569","url":"https://ijcai.org/proceedings/2024/569","pdf":"https://ijcai.org/proceedings/2024/0569.pdf","markdown":"https://ijcai.org/proceedings/2024/569.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/569","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Machine Learning","track":"Main Track","number":569,"pages":{"first":5144,"last":5152},"keywords":["Machine Learning: ML: Multi-view learning","Machine Learning: ML: Matrix/tensor methods","Machine Learning: ML: Classification","Machine Learning: ML: Clustering"],"videos":[],"references":[{"position":1,"raw":"[Abavisani and Patel, 2018] Mahdi Abavisani and Vishal M Patel. 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