{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T23:28:06Z","timestamp":1771025286085,"version":"3.50.1"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T00:00:00Z","timestamp":1763078400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T00:00:00Z","timestamp":1763078400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2026,3]]},"DOI":"10.1007\/s40314-025-03482-7","type":"journal-article","created":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T14:11:25Z","timestamp":1763129485000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Improved graph-based semi-supervised learning schemes"],"prefix":"10.1007","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5389-1220","authenticated-orcid":false,"given":"Farid","family":"Bozorgnia","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,11,14]]},"reference":[{"key":"3482_CR1","unstructured":"Alcal\u00e1-Fdez J, Fern\u00e1ndez A, Luengo J,\u00a0Derrac J, Garc\u00eda S, S\u00e1nchez L, Herrera F (2011) Keel data-mining software tool: Data set repository, integration of algorithms and experimental analysis framework. J Multiple-Val Logic Soft Comput 17:255\u2013287"},{"key":"3482_CR2","doi-asserted-by":"crossref","unstructured":"Ando RK, Zhang T (2007) Learning on graph with Laplacian regularization. In: Advances in Neural Information Processing Systems, pages 25\u201332","DOI":"10.7551\/mitpress\/7503.003.0009"},{"key":"3482_CR3","first-page":"2399","volume":"7","author":"M Belkin","year":"2006","unstructured":"Belkin M, Niyogi P, Sindhwani V (2006) Manifold regularization: a geometric framework for learning from labeled and unlabeled examples. J Mach Learn Res 7:2399\u20132434","journal-title":"J Mach Learn Res"},{"key":"3482_CR4","unstructured":"Belkin M, Niyogi P (2002) Using manifold structure for partially labelled classification. In Advances in Neural Information Processing Systems"},{"key":"3482_CR5","unstructured":"Boz S, Alacaoglu A, Ozkural E, Cevher V (2022) Adaptive label propagation for learning with few labeled nodes. In Proceedings of the International Conference on Machine Learning (ICML)"},{"key":"3482_CR6","doi-asserted-by":"crossref","unstructured":"Bozorgnia F, Fotouhi M, Arakelyan A, Elmoataz A (2023) Graph based semi-supervised learning using spatial segregation theory. J Comput Sci 74","DOI":"10.1016\/j.jocs.2023.102153"},{"key":"3482_CR7","doi-asserted-by":"crossref","unstructured":"Calder J (2018) The game theoretic p-laplacian and semisupervised learning with few labels. Nonlinearity 32(1)","DOI":"10.1088\/1361-6544\/aae949"},{"issue":"3","key":"3482_CR8","doi-asserted-by":"publisher","first-page":"1111","DOI":"10.1007\/s00245-019-09637-3","volume":"82","author":"J Calder","year":"2020","unstructured":"Calder J, Slep\u010dev D (2020) Properly-weighted graph laplacian for semi-supervised learning. Appl Math Optim 82(3):1111\u20131159","journal-title":"Appl Math Optim"},{"key":"3482_CR9","unstructured":"Calder J, Cook B,Thorpe M, Slep\u010dev D (2020) Poisson learning: Graph based semi-supervised learning at very low label rates. In Proceedings of the 37th International Conference on Machine Learning, volume 119 of PMLR, pages 1306\u20131316"},{"key":"3482_CR10","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/9780262033589.001.0001","volume-title":"Semi-supervised learning","author":"O Chapelle","year":"2006","unstructured":"Chapelle O, Sch\u00f6lkopf B, Zien A (2006) Semi-supervised learning. MIT Press, Cambridge"},{"key":"3482_CR11","unstructured":"Cheng W, Zou D, Zhang Q, Wang X (2022) Graph random neural networks for semi-supervised learning on graphs. In Advances in Neural Information Processing Systems"},{"key":"3482_CR12","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1016\/j.neucom.2019.12.130","volume":"408","author":"Y Chonga","year":"2020","unstructured":"Chonga Y, Dinga Y, Yanb Q, Pana S (2020) Graph-based semi-supervised learning: a review. Neurocomputing 408:216\u2013230","journal-title":"Neurocomputing"},{"key":"3482_CR13","doi-asserted-by":"crossref","unstructured":"Grover A, Leskovec J (2016) node2vec: Scalable feature learning for networks. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 855\u2013864. ACM","DOI":"10.1145\/2939672.2939754"},{"key":"3482_CR14","unstructured":"Hamilton WL, Ying R, Leskovec J (2017) Inductive representation learning on large graphs. In Advances in neural information processing systems, pages 1024\u20131034"},{"key":"3482_CR15","unstructured":"Ju, W, Liu S, Sun P, Wang X, Wang L (2024) A survey of data-efficient graph learning. arXiv preprint arXiv:2402.00447"},{"key":"3482_CR16","unstructured":"Kipf TN, Welling M (2016) Variational graph auto-encoders. arXiv preprint arXiv:1611.07308"},{"key":"3482_CR17","unstructured":"Kipf TN, Welling M (2017) Semi-supervised classification with graph convolutional networks. In International Conference on Learning Representations (ICLR)"},{"key":"3482_CR18","doi-asserted-by":"publisher","first-page":"1345","DOI":"10.1007\/s10994-021-05975-y","volume":"110","author":"J Liang","year":"2021","unstructured":"Liang J, Cui J, Wang J, Wei W (2021) Graph-based semi-supervised learning via improving the quality of the graph dynamically. Mach Learn 110:1345\u20131388","journal-title":"Mach Learn"},{"key":"3482_CR19","doi-asserted-by":"crossref","unstructured":"Liu G, Wang T, Wang J, Xie M, Li J (2023) Semi-supervised graph imbalanced regression. In: Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 2221\u20132231. ACM","DOI":"10.1145\/3580305.3599497"},{"key":"3482_CR20","doi-asserted-by":"crossref","unstructured":"Perozzi B, Al-Rfou R, Skiena S(2014) Deepwalk: Online learning of social representations. In: Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 701\u2013710. ACM","DOI":"10.1145\/2623330.2623732"},{"issue":"3","key":"3482_CR21","doi-asserted-by":"publisher","first-page":"2085","DOI":"10.1137\/17M115222X","volume":"51","author":"D Slep\u010dev","year":"2019","unstructured":"Slep\u010dev D, Thorpe M (2019) Analysis of p-laplacian regularization in semisupervised learning. SIAM J Math Anal 51(3):2085\u20132120","journal-title":"SIAM J Math Anal"},{"issue":"10","key":"3482_CR22","first-page":"7821","volume":"34","author":"Z Song","year":"2023","unstructured":"Song Z, Yang X, Zenglin X, King I (2023) Graph-based semi-supervised learning: a comprehensive review. IEEE Trans Neural Netw Learn Syst 34(10):7821\u20137840","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"3482_CR23","doi-asserted-by":"crossref","unstructured":"Song Z, Yang X, Xu Z, King I (2022) Graph-based semi-supervised learning: a comprehensive review. IEEE Trans Neural Netw Learn Syst","DOI":"10.1109\/TNNLS.2022.3155478"},{"key":"3482_CR24","doi-asserted-by":"crossref","unstructured":"Streicher O, Gilboa G (2023) Graph laplacian for semi-supervised learning. In International Conference on Scale Space and Variational Methods in Computer Vision, Springer, pages 250\u2013262","DOI":"10.1007\/978-3-031-31975-4_19"},{"key":"3482_CR25","doi-asserted-by":"crossref","unstructured":"Subramanya A, Talukdar PP (2014) Graph-based semi-supervised learning, volume\u00a08 of Synthesis Lectures on Artificial Intelligence and Machine Learning","DOI":"10.1007\/978-3-031-01571-7"},{"key":"3482_CR26","doi-asserted-by":"publisher","unstructured":"Taban R, Nunes C, Oliveira MR (2023) Rm-smote: A new robust balancing technique. Available at Research Square, https:\/\/doi.org\/10.21203\/rs.3.rs-3256245\/v1","DOI":"10.21203\/rs.3.rs-3256245\/v1"},{"key":"3482_CR27","unstructured":"Veli\u010dkovi\u0106 P, Cucurull G, Casanova A, Romero A, Li\u00f2 P, Bengio Y (2018) Graph attention networks. In International Conference on Learning Representations (ICLR)"},{"key":"3482_CR28","volume":"145","author":"L Wang","year":"2023","unstructured":"Wang L, Zhang Y, Chen J, Chen H (2023) Fgbc: Flexible graph-based balanced classifier for semi-supervised node classification. Pattern Recogn 145:109793","journal-title":"Pattern Recogn"},{"key":"3482_CR29","unstructured":"Wang Z, Huang Y, Yang Y, Cui P, Sun X, Liu S (2023) From cluster assumption to graph convolution: Graph-based semi-supervised learning revisited. arXiv preprint arXiv:2309.13599"},{"key":"3482_CR30","first-page":"321","volume":"16","author":"D Zhou","year":"2004","unstructured":"Zhou D, Bousquet O, Lal TN, Weston J, Sch\u00f6lkopf B (2004) Learning with local and global consistency. In Advances in Neural Information Processing Systems (NeurIPS) 16:321\u2013328","journal-title":"In Advances in Neural Information Processing Systems (NeurIPS)"},{"key":"3482_CR31","unstructured":"Zhu X, Ghahramani Z, Lafferty JD (2003) Semisupervised learning using gaussian fields and harmonic functions. In Proceedings of the 20th International Conference on Machine Learning (ICML-03), pages 912\u2013919"},{"key":"3482_CR32","volume-title":"Introduction to semi-supervised learning","author":"X Zhu","year":"2022","unstructured":"Zhu X, Goldberg AB (2022) Introduction to semi-supervised learning. Springer, Berlin"},{"key":"3482_CR33","doi-asserted-by":"publisher","first-page":"817","DOI":"10.3390\/rs10060817","volume":"10","author":"B Zu","year":"2018","unstructured":"Zu B, Xia K, Du W, Li Y, Ali A, Chakraborty S (2018) Classification of hyperspectral images with robust regularized block low-rank discriminant analysis. Remote Sens 10:817","journal-title":"Remote Sens"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-025-03482-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-025-03482-7","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-025-03482-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T04:46:18Z","timestamp":1769834778000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-025-03482-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,14]]},"references-count":33,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,3]]}},"alternative-id":["3482"],"URL":"https:\/\/doi.org\/10.1007\/s40314-025-03482-7","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,14]]},"assertion":[{"value":"11 March 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 September 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 October 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 November 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The author declares that there are no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"83"}}