{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T19:17:15Z","timestamp":1792783035293,"version":"4.5.0"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2026,8,29]],"date-time":"2026-08-29T00:00:00Z","timestamp":1787961600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,8,29]],"date-time":"2026-08-29T00:00:00Z","timestamp":1787961600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Universidad del Pa\u00eds Vasco","id":[{"id":"https:\/\/ror.org\/000xsnr85","id-type":"ROR","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Data Min Knowl Disc"],"published-print":{"date-parts":[[2026,9]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Several classifiers operate exclusively on discrete variables, requiring continuous attributes to be preprocessed through discretization. Supervised discretization addresses this need by partitioning the domain of continuous variables into intervals that define a discretization policy. Federated learning, in turn, enables the collaborative training of global models without sharing raw data: users train local models and communicate their parameters to a central server, which aggregates them into a global model. A key challenge in this setting is achieving performance comparable to centralized methods while minimizing communication overhead. In this work, we propose a federated discretization framework that computes a global discretization policy in a single communication round. Each user estimates Gaussian mixture models for the continuous variables and transmits their parameters-referred to as representatives-to the server. The server then applies a discretization algorithm to these representatives to derive a global policy, which is subsequently distributed back to the users. The proposed framework accommodates multiple discretization strategies; specifically, we present federated adaptations of equal-width, equal-frequency, entropy-based, and kernel density-based methods. Experiments conducted on ten benchmark datasets demonstrate that the proposed framework achieves performance comparable to centralized discretization approaches, with the kernel density-based and equal-frequency variants yielding the most competitive results.<\/jats:p>","DOI":"10.1007\/s10618-026-01247-2","type":"journal-article","created":{"date-parts":[[2026,8,29]],"date-time":"2026-08-29T09:14:37Z","timestamp":1787994877000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Federated discretization for supervised classification"],"prefix":"10.1007","volume":"40","author":[{"given":"Jose Luis","family":"Flores","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Borja","family":"Calvo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aritz","family":"P\u00e9rez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,8,29]]},"reference":[{"key":"1247_CR1","doi-asserted-by":"publisher","unstructured":"Bay SD (2000) Multivariate discretization of continuous variables for set mining. In: Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 315\u2013319. Association for Computing Machinery, New York, NY, USA. https:\/\/doi.org\/10.1145\/347090.347159","DOI":"10.1145\/347090.347159"},{"key":"1247_CR2","doi-asserted-by":"publisher","unstructured":"Bielza C, Larra\u00f1aga P (2014) Discrete bayesian network classifiers: a survey. ACM Comput Surv 47(1): https:\/\/doi.org\/10.1145\/2576868","DOI":"10.1145\/2576868"},{"key":"1247_CR3","unstructured":"Choudhury O, Park Y, Salonidis T, Gkoulalas-Divanis A, Sylla I, Das A (2020) Predicting adverse drug reactions on distributed health data using federated learning. In: AMIA Annual Symposium Proceedings, vol. 2019. Chicago, USA\/Online, pp. 313\u2013322. https:\/\/europepmc.org\/articles\/PMC7153050"},{"key":"1247_CR4","doi-asserted-by":"publisher","unstructured":"Collins L, Hassani H, Mokhtari A, Shakkottai S (2021) Exploiting shared representations for personalized federated learning. In: Meila M, Zhang T (eds) Proceedings of the 38th International Conference on Machine Learning. Proceedings of Machine Learning Research, vol. 139, pp. 2089\u20132099. PMLR, Red Hook, NY, USA. https:\/\/doi.org\/10.48550\/arXiv.2102.07078","DOI":"10.48550\/arXiv.2102.07078"},{"issue":"1","key":"1247_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","volume":"39","author":"AP Dempster","year":"1977","unstructured":"Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J Roy Stat Soc: Ser B (Methodol) 39(1):1\u201322. https:\/\/doi.org\/10.1111\/j.2517-6161.1977.tb01600.x","journal-title":"J Roy Stat Soc: Ser B (Methodol)"},{"key":"1247_CR6","unstructured":"Fayyad UM, Irani KB (1993) Multi-interval discretization of continuous-valued attributes for classification learning. International Joint Conference on Artificial Intelligence. Chamb\u00e9ry, France"},{"key":"1247_CR7","doi-asserted-by":"publisher","unstructured":"Feng J, Rong C, Sun F, Guo D, Li Y (2020) PMF: a privacy-preserving human mobility prediction framework via federated learning. In: ACM International Conference on Interactive, Mobile, Wearable and Ubiquitous Technologies, vol. 4. Association for Computing Machinery, Canc\u00fan, M\u00e9xico\/Online. https:\/\/doi.org\/10.1145\/3381006","DOI":"10.1145\/3381006"},{"key":"1247_CR8","doi-asserted-by":"publisher","unstructured":"Ferrandiz S, Boull\u00e9 M (2005) Multivariate discretization by recursive supervised bipartition of graph. In: Perner P, Imiya A (eds) Machine learning and data mining in pattern recognition, pp. 253\u2013264. Springer, Berlin, Heidelberg. https:\/\/doi.org\/10.1007\/11510888_25","DOI":"10.1007\/11510888_25"},{"key":"1247_CR9","unstructured":"Flores JL, Perez BCA (2026) Supplementary experimental results for federated learning discretization models in non-iid settings and multiple classifiers. https:\/\/github.com\/scpflbaj\/federated_discretization. Accessed: 2026-02-26"},{"key":"1247_CR10","doi-asserted-by":"publisher","first-page":"496","DOI":"10.1016\/j.patrec.2019.10.016","volume":"128","author":"JL Flores","year":"2019","unstructured":"Flores JL, Calvo B, P\u00e9rez A (2019) Supervised non-parametric discretization based on kernel density estimation. Pattern Recogn Lett 128:496\u2013504. https:\/\/doi.org\/10.1016\/j.patrec.2019.10.016","journal-title":"Pattern Recogn Lett"},{"key":"1247_CR11","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1016\/j.patrec.2022.07.008","volume":"161","author":"JL Flores","year":"2022","unstructured":"Flores JL, Calvo B, P\u00e9rez A (2022) Non-parametric discretization for probabilistic labeled data. Pattern Recogn Lett 161:52\u201358. https:\/\/doi.org\/10.1016\/j.patrec.2022.07.008","journal-title":"Pattern Recogn Lett"},{"key":"1247_CR12","doi-asserted-by":"publisher","unstructured":"Garc\u00eda MNM, Lucas JP, Batista VFL, Vivian FL, Mart\u00edn MJP (2010) Multivariate discretization for associative classification in a sparse data application domain. In: Romay MG, Corchado E, Sebastian MTG (eds) Hybrid artificial intelligence systems, pp. 104\u2013111. Springer, Berlin, Heidelberg. https:\/\/doi.org\/10.1007\/978-3-642-13769-3_13","DOI":"10.1007\/978-3-642-13769-3_13"},{"issue":"10","key":"1247_CR13","doi-asserted-by":"publisher","first-page":"2044","DOI":"10.1016\/j.ins.2009.12.010","volume":"180","author":"S Garc\u00eda","year":"2010","unstructured":"Garc\u00eda S, Fern\u00e1ndez A, Luengo J, Herrera F (2010) Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: experimental analysis of power. Inf Sci 180(10):2044\u20132064. https:\/\/doi.org\/10.1016\/j.ins.2009.12.010","journal-title":"Inf Sci"},{"key":"1247_CR14","doi-asserted-by":"publisher","unstructured":"Han X, Yu H, Gu H (2019) Visual inspection with federated learning. In: Image analysis and recognition, pp. 52\u201364. Springer, Berlin, Heidelberg. https:\/\/doi.org\/10.1007\/978-3-030-27272-2_5","DOI":"10.1007\/978-3-030-27272-2_5"},{"key":"1247_CR15","doi-asserted-by":"publisher","unstructured":"Hu B, Gao Y, Liu L, Ma H (2018) Federated region-learning: an edge computing based framework for urban environment sensing. In: IEEE Global Communications Conference, Abu Dhabi, United Arab Emirates, pp. 1\u20137. https:\/\/doi.org\/10.1109\/GLOCOM.2018.8647649","DOI":"10.1109\/GLOCOM.2018.8647649"},{"key":"1247_CR16","unstructured":"Kohavi R, Sahami M (1996) Error-based and entropy-based discretization of continuous features. In: Proceedings of the International Conference on Knowledge Discovery and Data Mining, pp. 114\u2013119. AAAI Press, Portland, Oregon. https:\/\/www.aaai.org\/Papers\/KDD\/1996\/KDD96-019.pdf"},{"key":"1247_CR17","doi-asserted-by":"publisher","unstructured":"Kone\u010dn\u00fd J, McMahan HB, Ramage D, Richt\u00e1rik P (2016) Federated optimization: distributed machine learning for on-device intelligence. CoRR https:\/\/doi.org\/10.48550\/arXiv.1610.02527","DOI":"10.48550\/arXiv.1610.02527"},{"key":"1247_CR18","doi-asserted-by":"publisher","unstructured":"Kone\u010dn\u00fd J, McMahan HB, Yu FX, Richt\u00e1rik P, Suresh AT, Bacon D (2016) Federated learning: strategies for improving communication efficiency. CoRR https:\/\/doi.org\/10.48550\/arXiv.1610.05492","DOI":"10.48550\/arXiv.1610.05492"},{"key":"1247_CR19","doi-asserted-by":"publisher","unstructured":"Kwatra S, Torra V (2024) DISCOLEAF: personalized discretization of continuous attributes for learning with federated decision trees. In: Domingo-Ferrer J, \u00d6nen M (eds) Privacy in statistical databases, pp. 344\u2013357. Springer, Cham. https:\/\/doi.org\/10.1007\/978-3-031-69651-0_23","DOI":"10.1007\/978-3-031-69651-0_23"},{"issue":"12","key":"1247_CR20","doi-asserted-by":"publisher","first-page":"1462","DOI":"10.1631\/FITEE.1800573","volume":"19","author":"J-H Li","year":"2018","unstructured":"Li J-H (2018) Cyber security meets artificial intelligence: a survey. Front Inf Technol Electron Eng 19(12):1462. https:\/\/doi.org\/10.1631\/FITEE.1800573","journal-title":"Frontiers of Information Technology & Electronic Engineering"},{"key":"1247_CR21","doi-asserted-by":"publisher","unstructured":"Liu D, Dligach D, Miller T (2019) Two-stage federated phenotyping and patient representation learning. BioNLP Workshop and Shared Task. pp 283\u2013291. https:\/\/doi.org\/10.18653\/v1\/W19-5030","DOI":"10.18653\/v1\/W19-5030"},{"key":"1247_CR22","doi-asserted-by":"publisher","unstructured":"Manzoorand HU, Shabbirand A, Chenand A, Flynnand D, Zoha A (2024) A survey of security strategies in federated learning: defending models, data, and privacy. Future Internet 16(10): https:\/\/doi.org\/10.3390\/fi16100374","DOI":"10.3390\/fi16100374"},{"issue":"1","key":"1247_CR23","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1002\/0471721182","volume":"6","author":"GJ McLachlan","year":"2019","unstructured":"McLachlan GJ, Lee SX, Rathnayake SI (2019) Finite mixture models. Annual review of statistics and its application 6(1):355\u2013378. https:\/\/doi.org\/10.1002\/0471721182","journal-title":"Annual review of statistics and its application"},{"key":"1247_CR24","doi-asserted-by":"publisher","unstructured":"McMahan B, Moore E, Ramage D, Hampson S, Arcas BA (2017) Communication-efficient learning of deep networks from decentralized data. In: International Conference on Artificial Intelligence and Statistics (AISTATS). Proceedings of Machine Learning Research, vol. 54, pp. 1273\u20131282. PMLR, Fort Lauderdale, Florida, USA. https:\/\/doi.org\/10.48550\/arXiv.1602.05629","DOI":"10.48550\/arXiv.1602.05629"},{"key":"1247_CR25","doi-asserted-by":"publisher","unstructured":"Murphy KP (2012) Machine learning: a probabilistic perspective. MIT Press, Cambridge, MA. https:\/\/doi.org\/10.1080\/09332480.2014.914768","DOI":"10.1080\/09332480.2014.914768"},{"key":"1247_CR26","doi-asserted-by":"publisher","unstructured":"Pfohl SR, Dai AM, Heller KA (2019) Federated and differentially private learning for electronic health records. arXiv preprint arXiv:1911.05839. https:\/\/doi.org\/10.48550\/arxiv.1911.05861","DOI":"10.48550\/arxiv.1911.05861"},{"key":"1247_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.ress.2023.109130","volume":"233","author":"K Sayaka","year":"2023","unstructured":"Sayaka K, Sharareh T (2023) A comparison study of centralized and decentralized federated learning approaches utilizing the transformer architecture for estimating remaining useful life. Reliab Eng Syst Saf 233:109130. https:\/\/doi.org\/10.1016\/j.ress.2023.109130","journal-title":"Reliability Engineering & System Safety"},{"key":"1247_CR28","doi-asserted-by":"publisher","unstructured":"Silva S, Gutman BA, Romero E, Thompson PM, Altmann A, Lorenzi M (2019) Federated learning in distributed medical databases: Meta-analysis of large-scale subcortical brain data. In: IEEE International Symposium on Biomedical Imaging. Proceedings-International Symposium on Biomedical Imaging, pp. 270\u2013274. IEEE Computer Society, Venice, Italy. https:\/\/doi.org\/10.1109\/ISBI.2019.8759317","DOI":"10.1109\/ISBI.2019.8759317"},{"key":"1247_CR29","doi-asserted-by":"publisher","unstructured":"Sozinov K, Vlassov V, Girdzijauskas S (2018) Human activity recognition using federated learning. In: IEEE International Conference on Parallel & Distributed Processing with Applications, Melbourne, Australia, pp. 1103\u20131111. https:\/\/doi.org\/10.1109\/BDCloud.2018.00164","DOI":"10.1109\/BDCloud.2018.00164"},{"issue":"12","key":"1247_CR30","doi-asserted-by":"publisher","first-page":"2092","DOI":"10.1080\/02664763.2020.1784853","volume":"48","author":"P Sulewski","year":"2021","unstructured":"Sulewski P (2021) Equal-bin-width histogram versus equal-bin-count histogram. J Appl Stat 48(12):2092\u20132111. https:\/\/doi.org\/10.1080\/02664763.2020.1784853","journal-title":"J Appl Stat"},{"key":"1247_CR31","doi-asserted-by":"publisher","unstructured":"Sun H, Wang Z, Huang Y, Ye J (2022) Privacy-preserving vertical federated logistic regression without trusted third-party coordinator. In: International Conference on Machine Learning and Soft Computing, pp. 132\u2013138. Association for Computing Machinery, New York, NY, USA. https:\/\/doi.org\/10.1145\/3523150.3523171","DOI":"10.1145\/3523150.3523171"},{"key":"1247_CR32","doi-asserted-by":"publisher","unstructured":"Tanuwidjaja H, Choi R, Kim K (2019) A survey on deep learning techniques for privacy-preserving. In: Chen X, Huang X, Zhang J (eds) Machine learning for cyber security, pp. 29\u201346. Springer, Cham. https:\/\/doi.org\/10.1007\/978-3-030-30619-9_4","DOI":"10.1007\/978-3-030-30619-9_4"},{"key":"1247_CR33","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/3377454","volume":"53","author":"J Verbraeken","year":"2019","unstructured":"Verbraeken J, Wolting M, Katzy J, Kloppenburg J, Verbelen T, Rellermeyer JS (2019) A survey on distributed machine learning. ACM Comput Surv (CSUR) 53:1\u201333. https:\/\/doi.org\/10.1145\/3377454","journal-title":"ACM Computing Surveys (CSUR)"},{"key":"1247_CR34","doi-asserted-by":"publisher","unstructured":"Wang A, Wang C, Bi M, Xu J (2018) A review of privacy-preserving machine learning classification. In: Cloud Computing and Security, pp. 671\u2013682.https:\/\/doi.org\/10.1007\/978-3-030-00015-8_58","DOI":"10.1007\/978-3-030-00015-8_58"},{"key":"1247_CR35","doi-asserted-by":"publisher","unstructured":"Wang H, Yurochkin M, Sun Y, Papailiopoulos D, Khazaeni Y (2020) Federated learning with matched averaging. In: International Conference on Learning Representations (ICLR). https:\/\/doi.org\/10.48550\/arXiv.2002.06440","DOI":"10.48550\/arXiv.2002.06440"},{"key":"1247_CR36","doi-asserted-by":"publisher","unstructured":"Xiong N, Punnekkat S (2023) Tiny federated learning with bayesian classifiers. In: 2023 IEEE International Symposium on Industrial Electronics (ISIE), Helsinki-Espoo, Finland, pp. 1\u20136.https:\/\/doi.org\/10.1109\/ISIE51358.2023.10228115","DOI":"10.1109\/ISIE51358.2023.10228115"},{"key":"1247_CR37","doi-asserted-by":"publisher","unstructured":"Yang T, Andrew G, Eichner H, Sun H, Li W, Kong N, Ramage D, Beaufays F (2018) Applied federated learning: improving google keyboard query suggestions. In: International Conference on Neural Information Processing Systems (NIPS). NeurIPS \u201918, pp. 4350\u20134360. Curran Associates Inc., Montr\u00e9al, Canada.https:\/\/doi.org\/10.48550\/arXiv.1812.02903","DOI":"10.48550\/arXiv.1812.02903"},{"key":"1247_CR38","doi-asserted-by":"publisher","unstructured":"Yang W, Zhang Y, Ye K, Li L, Xu C-Z (2019) FFD: a federated learning based method for credit card fraud detection. In: Chen K, Seshadri S, Zhang LJ (eds) Big Data \u2013 BigData 2019, pp. 18\u201332. Springer, Cham.https:\/\/doi.org\/10.1007\/978-3-030-23551-2_2","DOI":"10.1007\/978-3-030-23551-2_2"},{"key":"1247_CR39","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2021.106775","volume":"216","author":"C Zhang","year":"2021","unstructured":"Zhang C, Xie Y, Bai H, Yu B, Li W, Gao Y (2021) A survey on federated learning. Knowl-Based Syst 216:106775. https:\/\/doi.org\/10.1016\/j.knosys.2021.106775","journal-title":"Knowl-Based Syst"}],"container-title":["Data Mining and Knowledge Discovery"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10618-026-01247-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10618-026-01247-2","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10618-026-01247-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T03:04:51Z","timestamp":1790823891000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10618-026-01247-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,29]]},"references-count":39,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2026,9]]}},"alternative-id":["1247"],"URL":"https:\/\/doi.org\/10.1007\/s10618-026-01247-2","relation":{},"ISSN":["1384-5810","1573-756X"],"issn-type":[{"value":"1384-5810","type":"print"},{"value":"1573-756X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,29]]},"assertion":[{"value":"29 September 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 July 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 August 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no conflict of interest.","order":1,"name":"Ethics","label":"Conflict of interest","group":{"name":"EthicsHeading","label":"Declarations"}}],"article-number":"85"}}