{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:44:33Z","timestamp":1760060673790,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T00:00:00Z","timestamp":1757548800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Liaoning Provincial Natural Science Foundation of China","award":["2022-MS-420","2023JH2\/101300134","2024-MSLH-203","2022JH13\/10200047","2023JSZ11"],"award-info":[{"award-number":["2022-MS-420","2023JH2\/101300134","2024-MSLH-203","2022JH13\/10200047","2023JSZ11"]}]},{"name":"Key Laboratory Project of Intelligent Application of Liaoning Province Public Security Big Data","award":["2022-MS-420","2023JH2\/101300134","2024-MSLH-203","2022JH13\/10200047","2023JSZ11"],"award-info":[{"award-number":["2022-MS-420","2023JH2\/101300134","2024-MSLH-203","2022JH13\/10200047","2023JSZ11"]}]},{"name":"technical research program project of the Ministry of Public Security","award":["2022-MS-420","2023JH2\/101300134","2024-MSLH-203","2022JH13\/10200047","2023JSZ11"],"award-info":[{"award-number":["2022-MS-420","2023JH2\/101300134","2024-MSLH-203","2022JH13\/10200047","2023JSZ11"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>ELM is an innovative learning algorithm that minimizes output error by only finding optimal output weights. Meta-learning is composed of base ELMs and exhibits good generalization. To improve its performance further by introducing orthogonal constraints into the base ELMs and \u201ctop\u201d ELM, we propose a novel Meta-ELM with orthogonal constraints (Meta-QEC-ELM). Because of the particularity of the Meta-ELM, its orthogonal constraint problem is the quadratic equality constraint problem\u2014that is, a one-column Procrustes problem\u2014and it can preserve much more information from feature space to output subspace. The experimental results show that the Meta-QEC-ELM is both effective and feasible.<\/jats:p>","DOI":"10.3390\/sym17091515","type":"journal-article","created":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T07:51:46Z","timestamp":1757577106000},"page":"1515","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Novel Meta-ELM with Orthogonal Constraints for Regression Problems"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4929-9715","authenticated-orcid":false,"given":"Licheng","family":"Cui","sequence":"first","affiliation":[{"name":"School of Cybersecurity, Liaoning Police Academy, Dalian 116036, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7191-2280","authenticated-orcid":false,"given":"Huawei","family":"Zhai","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Dalian Maritime University, Dalian 116026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/s10462-013-9405-z","article-title":"Extreme Learning Machine: Algorithm, Theory and Applications","volume":"44","author":"Ding","year":"2015","journal-title":"Artif. 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