{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T04:56:38Z","timestamp":1775883398786,"version":"3.50.1"},"reference-count":45,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"2","license":[{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"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":["12471482"],"award-info":[{"award-number":["12471482"]}],"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":["12571492"],"award-info":[{"award-number":["12571492"]}],"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":["12031003"],"award-info":[{"award-number":["12031003"]}],"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":["12271117"],"award-info":[{"award-number":["12271117"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Comput. Intell. Mag."],"published-print":{"date-parts":[[2026,5]]},"DOI":"10.1109\/mci.2026.3655677","type":"journal-article","created":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T19:44:33Z","timestamp":1775763873000},"page":"84-98","source":"Crossref","is-referenced-by-count":0,"title":["Graph Regularization for High Order Neural Networks: Boundedness, Convergence, and Enhanced Performance With Entropy Error Function [Research Frontier]"],"prefix":"10.1109","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1017-3496","authenticated-orcid":false,"given":"Qinwei","family":"Fan","sequence":"first","affiliation":[{"name":"School of Mathematics and Information Science, Guangzhou University, Guangzhou, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-8875-2782","authenticated-orcid":false,"given":"Qianru","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Science, Xi&#x2019;an Polytechnic University, Xi&#x2019;an, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6622-534X","authenticated-orcid":false,"given":"Jacek M.","family":"Zurada","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Louisville, Louisville, KY, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7207-3183","authenticated-orcid":false,"given":"Jigen","family":"Peng","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, Guangzhou University, Guangzhou, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7238-2456","authenticated-orcid":false,"given":"Haiyang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, Guangzhou University, Guangzhou, China"}]}],"member":"263","reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2024.104078"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2023.103951"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-020-04899-3"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-021-05781-6"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1364\/AO.26.004972"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2021.3074654"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2022.3208604"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022967523886"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2022.105030"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1109\/72.238319"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1109\/72.377979"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/TNSE.2020.3037039"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1109\/JSAC.2016.2525598"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2023.3319989"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2013.2257845"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1007\/s11063-019-10135-4"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-012-0915-4"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1007\/s11063-018-9835-3"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.7763\/IJCTE.2016.V8.1037"},{"key":"ref20","first-page":"5","article-title":"Improving error back propagation algorithm by using cross entropy error function and adaptive learning rate","volume":"161","author":"Elsadek","year":"2017","journal-title":"Int. J. Comput. Appl."},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.21437\/interspeech.2013-436"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2020.02.113"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1007\/s11063-020-10374-w"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1162\/089976600300015763"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2015.2478405"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2017.06.057"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1109\/LGRS.2022.3168015"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.3390\/rs15061670"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.4208\/eajam.2023-025.080823"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2019.2893266"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2020.12.014"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2013.10.023"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2018.06.046"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2005.00503.x"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2024.3371592"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2023.3285215"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2020.3016143"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2024.3370918"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2025.3616350"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1109\/JSTARS.2022.3191692"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1109\/JBHI.2022.3148286"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2010.231"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1109\/LGRS.2020.3027055"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2015.2493537"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2022.05.121"}],"container-title":["IEEE Computational Intelligence Magazine"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx8\/10207\/11478563\/11478573.pdf?arnumber=11478573","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T04:27:29Z","timestamp":1775881649000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/11478573\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5]]},"references-count":45,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.1109\/mci.2026.3655677","relation":{},"ISSN":["1556-603X","1556-6048"],"issn-type":[{"value":"1556-603X","type":"print"},{"value":"1556-6048","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5]]}}}