{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T04:15:45Z","timestamp":1775103345165,"version":"3.50.1"},"publisher-location":"California","reference-count":0,"publisher":"International Joint Conferences on Artificial Intelligence Organization","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:p>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\u2014an 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.<\/jats:p>","DOI":"10.24963\/ijcai.2025\/675","type":"proceedings-article","created":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T08:10:40Z","timestamp":1758269440000},"page":"6066-6074","source":"Crossref","is-referenced-by-count":2,"title":["Beyond Low-rankness: Guaranteed Matrix Recovery via Modified Nuclear Norm"],"prefix":"10.24963","author":[{"given":"Jiangjun","family":"Peng","sequence":"first","affiliation":[{"name":"Northwestern Polytechnical University"}]},{"given":"Yisi","family":"Luo","sequence":"additional","affiliation":[{"name":"Xi'an Jiaotong Univerisity"}]},{"given":"Xiangyong","family":"Cao","sequence":"additional","affiliation":[{"name":"Xi'an Jiaotong Univerisity"}]},{"given":"Shuang","family":"Xu","sequence":"additional","affiliation":[{"name":"Northwestern Polytechnical University"}]},{"given":"Deyu","family":"Meng","sequence":"additional","affiliation":[{"name":"Xi'an Jiaotong Univerisity"}]}],"member":"10584","event":{"name":"Thirty-Fourth International Joint Conference on Artificial Intelligence {IJCAI-25}","theme":"Artificial Intelligence","location":"Montreal, Canada","acronym":"IJCAI-2025","number":"34","sponsor":["International Joint Conferences on Artificial Intelligence Organization (IJCAI)"],"start":{"date-parts":[[2025,8,16]]},"end":{"date-parts":[[2025,8,22]]}},"container-title":["Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence"],"original-title":[],"deposited":{"date-parts":[[2025,9,23]],"date-time":"2025-09-23T11:34:49Z","timestamp":1758627289000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ijcai.org\/proceedings\/2025\/675"}},"subtitle":[],"proceedings-subject":"Artificial Intelligence Research Articles","short-title":[],"issued":{"date-parts":[[2025,9]]},"references-count":0,"URL":"https:\/\/doi.org\/10.24963\/ijcai.2025\/675","relation":{},"subject":[],"published":{"date-parts":[[2025,9]]}}}