{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T19:17:11Z","timestamp":1769109431255,"version":"3.49.0"},"reference-count":39,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"6","license":[{"start":{"date-parts":[[2024,6,1]],"date-time":"2024-06-01T00:00:00Z","timestamp":1717200000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2024,6,1]],"date-time":"2024-06-01T00:00:00Z","timestamp":1717200000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2024,6,1]],"date-time":"2024-06-01T00:00:00Z","timestamp":1717200000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61972207"],"award-info":[{"award-number":["61972207"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U22B2062"],"award-info":[{"award-number":["U22B2062"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62172232"],"award-info":[{"award-number":["62172232"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Key R&D Program of China","award":["2021YFB2700900"],"award-info":[{"award-number":["2021YFB2700900"]}]},{"name":"Jiangsu Basic Research Programs-Natural Science Foundation","award":["BK20200039"],"award-info":[{"award-number":["BK20200039"]}]},{"DOI":"10.13039\/501100012246","name":"Priority Academic Program Development of Jiangsu Higher Education Institutions","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100012246","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Collaborative Innovation Center of Atmospheric Environment and Equipment Technology"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Pattern Anal. Mach. Intell."],"published-print":{"date-parts":[[2024,6]]},"DOI":"10.1109\/tpami.2024.3356661","type":"journal-article","created":{"date-parts":[[2024,1,22]],"date-time":"2024-01-22T18:40:21Z","timestamp":1705948821000},"page":"4160-4173","source":"Crossref","is-referenced-by-count":2,"title":["A New Sufficient & Necessary Condition for Testing Linear Separability Between Two Sets"],"prefix":"10.1109","volume":"46","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1949-7956","authenticated-orcid":false,"given":"Shuiming","family":"Zhong","sequence":"first","affiliation":[{"name":"School of Software, Engineering Research Center of Digital Forensics, Ministry of Education, Nanjing University of Information Science and Technology, Nanjing, Jiangsu, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-0649-881X","authenticated-orcid":false,"given":"Huan","family":"Lyu","sequence":"additional","affiliation":[{"name":"School of Computer Science, Nanjing University of Information Science and Technology, Nanjing, Jiangsu, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-5166-5460","authenticated-orcid":false,"given":"Xiaoxiang","family":"Lu","sequence":"additional","affiliation":[{"name":"College of Computer and Information, Hohai University, Nanjing, Jiangsu, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6764-5941","authenticated-orcid":false,"given":"Baowei","family":"Wang","sequence":"additional","affiliation":[{"name":"Engineering Research Center of Digital Forensics, Ministry of Education, the School of Computer Science, Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Nanjing University of Information Science and Technology, Nanjing, Jiangsu, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-4608-0560","authenticated-orcid":false,"given":"Dingcheng","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer Science, Nanjing University of Information Science and Technology, Nanjing, Jiangsu, China"}]}],"member":"263","reference":[{"key":"ref1","first-page":"18 583","article-title":"Measuring robustness to natural distribution shifts in image classification","volume":"33","author":"Taori","year":"2020","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref2","first-page":"7721","article-title":"Accuracy on the line: On the strong correlation between out-of-distribution and in-distribution generalization","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Miller"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2019.11.004"},{"key":"ref4","first-page":"87","article-title":"Predicted squared error: A criterion for automatic model selection","volume-title":"Self-Organizing Methods in Modeling","author":"Barron","year":"2020"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2018.2867638"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2021.12.014"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1145\/3447582"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2021.03.091"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1037\/h0042519"},{"key":"ref10","first-page":"1723","article-title":"Truncated back-propagation for bilevel optimization","volume-title":"Proc. 22nd Int. Conf. Artif. Intell. Statist.","author":"Shaban"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1007\/s10462-018-9614-6"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.cosrev.2021.100379"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1007\/BF00994018"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1109\/ISS1.2019.8908018"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.9781\/ijimai.2016.415"},{"key":"ref16","article-title":"An introduction to computational geometry","volume":"479","author":"Minsky","year":"1969","journal-title":"Cambridge Tiass., HIT"},{"key":"ref17","volume-title":"Convex Analysis","volume":"11","author":"Rockafellar","year":"1997"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1145\/235815.235821"},{"key":"ref19","article-title":"Computing the approximate convex hull in high dimensions","author":"Sartipizadeh","year":"2016"},{"key":"ref20","first-page":"460","article-title":"Visualizing the connection among convex hull, Voronoi diagram and delaunay triangulation","volume-title":"Proc. 37th Midwest Instruct. Comput. Symp.","author":"Fisher"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1145\/3430036.3430043"},{"issue":"2","key":"ref22","first-page":"48","article-title":"Convex hulls in image processing: A scoping review","volume":"6","author":"Jayaram","year":"2016","journal-title":"Amer. J. Intell. Syst."},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1109\/TCSVT.2019.2926165"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2015.2445291"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/ICPADS.2016.0164"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2011.01960.x"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR46437.2021.00868"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1111\/j.1469-1809.1936.tb02137.x"},{"key":"ref29","first-page":"xlvii","article-title":"Reported in: Analyse des travaux de i\u2019academie royale des sciences pendant i\u2019annee 1824","volume":"7","author":"Fourier","year":"1827","journal-title":"Partie mathematique, Histoire de l\u2019Academie Royale des Sci. de l\u2019Institut de France"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1956.11988793"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.2307\/1909468"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5610(94)00091-2"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1007\/s40314-021-01544-0"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1145\/1273496.1273598"},{"key":"ref35","first-page":"713","article-title":"A fast linear separability test by projection of positive points on subspaces","volume-title":"Proc. 24th Int. Conf. Mach. Learn.","author":"Yogananda"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2005.860871"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-012-0155-x"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1007\/BF01175656"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-018-3123-5"}],"container-title":["IEEE Transactions on Pattern Analysis and Machine Intelligence"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/34\/10522060\/10411108.pdf?arnumber=10411108","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,10]],"date-time":"2024-09-10T04:25:09Z","timestamp":1725942309000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/10411108\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6]]},"references-count":39,"journal-issue":{"issue":"6"},"URL":"https:\/\/doi.org\/10.1109\/tpami.2024.3356661","relation":{},"ISSN":["0162-8828","2160-9292","1939-3539"],"issn-type":[{"value":"0162-8828","type":"print"},{"value":"2160-9292","type":"electronic"},{"value":"1939-3539","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,6]]}}}