{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T15:02:21Z","timestamp":1781276541107,"version":"3.54.1"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"14","license":[{"start":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T00:00:00Z","timestamp":1757289600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T00:00:00Z","timestamp":1757289600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"the National Natural Science Foundation of China under Grant","award":["92467103, 92367302"],"award-info":[{"award-number":["92467103, 92367302"]}]},{"name":"the National Natural Science Foundation of China under Grant","award":["92467103, 92367302"],"award-info":[{"award-number":["92467103, 92367302"]}]},{"name":"the National Natural Science Foundation of China under Grant","award":["92467103, 92367302"],"award-info":[{"award-number":["92467103, 92367302"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Supercomput"],"DOI":"10.1007\/s11227-025-07728-3","type":"journal-article","created":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T16:21:56Z","timestamp":1757348516000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["FedCK:addressing label distribution skew in federated learning via clustering-efficient and knowledge distillation"],"prefix":"10.1007","volume":"81","author":[{"given":"Jinhua","family":"Chen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mengmeng","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xin","family":"He","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,9,8]]},"reference":[{"key":"7728_CR1","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","journal-title":"Knowl-Based Syst"},{"issue":"3","key":"7728_CR2","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1109\/MSP.2020.2975749","volume":"37","author":"T Li","year":"2020","unstructured":"Li T, Sahu AK, Talwalkar A, Smith V (2020) Federated learning: challenges, methods, and future directions. IEEE Signal Process Mag 37(3):50\u201360","journal-title":"IEEE Signal Process Mag"},{"key":"7728_CR3","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1016\/j.neucom.2021.07.098","volume":"465","author":"H Zhu","year":"2021","unstructured":"Zhu H, Xu J, Liu S, Jin Y (2021) Federated learning on non-iid data: a survey. Neurocomputing 465:371\u2013390","journal-title":"Neurocomputing"},{"issue":"2","key":"7728_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/3298981","volume":"10","author":"Q Yang","year":"2019","unstructured":"Yang Q, Liu Y, Chen T, Tong Y (2019) Federated machine learning: concept and applications. ACM Trans Intell Syst Technol (TIST) 10(2):1\u201319","journal-title":"ACM Trans Intell Syst Technol (TIST)"},{"issue":"3","key":"7728_CR5","first-page":"1","volume":"55","author":"DC Nguyen","year":"2022","unstructured":"Nguyen DC, Pham Q-V, Pathirana PN, Ding M, Seneviratne A, Lin Z, Dobre O, Hwang W-J (2022) Federated learning for smart healthcare: a survey. ACM Comput Surv(Csur) 55(3):1\u201337","journal-title":"ACM Comput Surv(Csur)"},{"issue":"6","key":"7728_CR6","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1038\/s42256-020-0186-1","volume":"2","author":"GA Kaissis","year":"2020","unstructured":"Kaissis GA, Makowski MR, R\u00fcckert D, Braren RF (2020) Secure, privacy-preserving and federated machine learning in medical imaging. Nature Mach Intell 2(6):305\u2013311","journal-title":"Nature Mach Intell"},{"issue":"5","key":"7728_CR7","doi-asserted-by":"publisher","first-page":"4475","DOI":"10.1109\/JIOT.2022.3218008","volume":"10","author":"L Li","year":"2022","unstructured":"Li L, Yu X, Cai X, He X, Liu Y (2022) Contract-theory-based incentive mechanism for federated learning in health crowdsensing. IEEE Internet Things J 10(5):4475\u20134489","journal-title":"IEEE Internet Things J"},{"key":"7728_CR8","doi-asserted-by":"publisher","DOI":"10.1016\/j.comnet.2021.108122","volume":"192","author":"Y Guo","year":"2021","unstructured":"Guo Y, Zhao Z, He K, Lai S, Xia J, Fan L (2021) Efficient and flexible management for industrial internet of things: a federated learning approach. Comput Netw 192:108122","journal-title":"Comput Netw"},{"issue":"8","key":"7728_CR9","doi-asserted-by":"publisher","first-page":"5605","DOI":"10.1109\/TII.2020.3034674","volume":"17","author":"W Sun","year":"2020","unstructured":"Sun W, Lei S, Wang L, Liu Z, Zhang Y (2020) Adaptive federated learning and digital twin for industrial internet of things. IEEE Trans Industr Inf 17(8):5605\u20135614","journal-title":"IEEE Trans Industr Inf"},{"key":"7728_CR10","unstructured":"McMahan B, Moore E, Ramage D, Hampson S, Arcas BA (2017) Communication-efficient learning of deep networks from decentralized data. In: Artificial Intelligence and Statistics, pp. 1273\u20131282. PMLR"},{"issue":"3","key":"7728_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/3625558","volume":"56","author":"M Ye","year":"2023","unstructured":"Ye M, Fang X, Du B, Yuen PC, Tao D (2023) Heterogeneous federated learning: state-of-the-art and research challenges. ACM Comput Surv 56(3):1\u201344","journal-title":"ACM Comput Surv"},{"key":"7728_CR12","doi-asserted-by":"publisher","first-page":"244","DOI":"10.1016\/j.future.2022.05.003","volume":"135","author":"X Ma","year":"2022","unstructured":"Ma X, Zhu J, Lin Z, Chen S, Qin Y (2022) A state-of-the-art survey on solving non-iid data in federated learning. Futur Gener Comput Syst 135:244\u2013258","journal-title":"Futur Gener Comput Syst"},{"issue":"1\u20132","key":"7728_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1561\/2200000083","volume":"14","author":"P Kairouz","year":"2021","unstructured":"Kairouz P, McMahan HB, Avent B, Bellet A, Bennis M, Bhagoji AN, Bonawitz K, Charles Z, Cormode G, Cummings R (2021) Advances and open problems in federated learning. Found Trends Machine Learn 14(1\u20132):1\u2013210","journal-title":"Found Trends Machine Learn"},{"key":"7728_CR14","unstructured":"Wang H, Yurochkin M, Sun Y, Papailiopoulos D, Khazaeni Y (2020) Federated learning with matched averaging. arXiv preprint arXiv:2002.06440"},{"issue":"12","key":"7728_CR15","doi-asserted-by":"publisher","first-page":"5806","DOI":"10.3390\/app12125806","volume":"12","author":"M Hong","year":"2022","unstructured":"Hong M, Kang S-K, Lee J-H (2022) Weighted averaging federated learning based on example forgetting events in label imbalanced non-iid. Appl Sci 12(12):5806","journal-title":"Appl Sci"},{"key":"7728_CR16","first-page":"7611","volume":"33","author":"J Wang","year":"2020","unstructured":"Wang J, Liu Q, Liang H, Joshi G, Poor HV (2020) Tackling the objective inconsistency problem in heterogeneous federated optimization. Adv Neural Inf Process Syst 33:7611\u20137623","journal-title":"Adv Neural Inf Process Syst"},{"key":"7728_CR17","first-page":"429","volume":"2","author":"T Li","year":"2020","unstructured":"Li T, Sahu AK, Zaheer M, Sanjabi M, Talwalkar A, Smith V (2020) Federated optimization in heterogeneous networks. Proc Mach Learn Syst 2:429\u2013450","journal-title":"Proc Mach Learn Syst"},{"issue":"4","key":"7728_CR18","doi-asserted-by":"publisher","first-page":"1520","DOI":"10.1007\/s11036-022-01978-8","volume":"27","author":"B Gong","year":"2022","unstructured":"Gong B, Xing T, Liu Z, Wang J, Liu X (2022) Adaptive clustered federated learning for heterogeneous data in edge computing. Mobile Netw Appl Cations 27(4):1520\u20131530","journal-title":"Mobile Netw Appl Cations"},{"issue":"7","key":"7728_CR19","doi-asserted-by":"publisher","first-page":"1660","DOI":"10.3390\/electronics12071660","volume":"12","author":"J Zhang","year":"2023","unstructured":"Zhang J, Li Z (2023) A clustered federated learning method of user behavior analysis based on non-iid data. Electronics 12(7):1660","journal-title":"Electronics"},{"issue":"15","key":"7728_CR20","doi-asserted-by":"publisher","first-page":"13303","DOI":"10.1109\/JIOT.2023.3262620","volume":"10","author":"C Ke\u00e7eci","year":"2023","unstructured":"Ke\u00e7eci C, Shaqfeh M, Al-Qahtani F, Ismail M, Serpedin E (2023) Clustered scheduling and communication pipelining for efficient resource management of wireless federated learning. IEEE Internet Things J 10(15):13303\u201313316","journal-title":"IEEE Internet Things J"},{"key":"7728_CR21","doi-asserted-by":"crossref","unstructured":"Diao Y, Li Q, He B (2024) Exploiting label skews in federated learning with model concatenation. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 38, pp 11784\u201311792","DOI":"10.1609\/aaai.v38i10.29063"},{"key":"7728_CR22","doi-asserted-by":"crossref","unstructured":"Gao L, Fu H, Li L, Chen Y, Xu M, Xu C-Z (2022) Feddc: Federated learning with non-iid data via local drift decoupling and correction. In: Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, pp 10112\u201310121","DOI":"10.1109\/CVPR52688.2022.00987"},{"key":"7728_CR23","doi-asserted-by":"crossref","unstructured":"Li Q, He B, Song D (2021) Model-contrastive federated learning. In: Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, pp 10713\u201310722","DOI":"10.1109\/CVPR46437.2021.01057"},{"key":"7728_CR24","doi-asserted-by":"crossref","unstructured":"Li X-C, Zhan D-C (2021) Fedrs: Federated learning with restricted softmax for label distribution non-iid data. In: Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining, pp 995\u20131005","DOI":"10.1145\/3447548.3467254"},{"key":"7728_CR25","doi-asserted-by":"publisher","first-page":"42082","DOI":"10.1109\/ACCESS.2023.3271517","volume":"11","author":"H Lee","year":"2023","unstructured":"Lee H, Seo D (2023) Fedlc: optimizing federated learning in non-iid data via label-wise clustering. IEEE Access 11:42082\u201342095","journal-title":"IEEE Access"},{"issue":"7","key":"7728_CR26","first-page":"1565","volume":"32","author":"X Wu","year":"2020","unstructured":"Wu X, Yao X, Wang C-L (2020) Fedscr: structure-based communication reduction for federated learning. IEEE Trans Parallel Distrib Syst 32(7):1565\u20131577","journal-title":"IEEE Trans Parallel Distrib Syst"},{"key":"7728_CR27","unstructured":"Acar DAE, Zhao Y, Navarro RM, Mattina M, Whatmough PN, Saligrama V (2021) Federated learning based on dynamic regularization. arXiv preprint arXiv:2111.04263"},{"key":"7728_CR28","unstructured":"Karimireddy SP, Kale S, Mohri M, Reddi SJ, Stich SU, Suresh AT (2019) Scaffold: stochastic controlled averaging for on-device federated learning. 2(6), arXiv:1910.06378"},{"issue":"9","key":"7728_CR29","doi-asserted-by":"publisher","first-page":"5226","DOI":"10.3934\/era.2023266","volume":"31","author":"Z Wang","year":"2023","unstructured":"Wang Z, Liu R, Xu J, Fu Y (2023) Fedsc: a federated learning algorithm based on client-side clustering. Electron Res Archive 31(9):5226\u20135249","journal-title":"Electron Res Archive"},{"key":"7728_CR30","doi-asserted-by":"crossref","unstructured":"Ruan Y, Joe-Wong C (2022) Fedsoft: Soft clustered federated learning with proximal local updating. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 36, pp 8124\u20138131","DOI":"10.1609\/aaai.v36i7.20785"},{"key":"7728_CR31","first-page":"19586","volume":"33","author":"A Ghosh","year":"2020","unstructured":"Ghosh A, Chung J, Yin D, Ramchandran K (2020) An efficient framework for clustered federated learning. Adv Neural Inf Process Syst 33:19586\u201319597","journal-title":"Adv Neural Inf Process Syst"},{"issue":"1","key":"7728_CR32","doi-asserted-by":"publisher","first-page":"481","DOI":"10.1007\/s11280-022-01046-x","volume":"26","author":"G Long","year":"2023","unstructured":"Long G, Xie M, Shen T, Zhou T, Wang X, Jiang J (2023) Multi-center federated learning: clients clustering for better personalization. World Wide Web 26(1):481\u2013500","journal-title":"World Wide Web"},{"issue":"1","key":"7728_CR33","doi-asserted-by":"publisher","first-page":"747","DOI":"10.1109\/JIOT.2022.3203233","volume":"10","author":"X You","year":"2022","unstructured":"You X, Liu X, Jiang N, Cai J, Ying Z (2022) Reschedule gradients: temporal non-iid resilient federated learning. IEEE Internet Things J 10(1):747\u2013762","journal-title":"IEEE Internet Things J"},{"key":"7728_CR34","doi-asserted-by":"crossref","unstructured":"Jang J, Ha H, Jung D, Yoon S (2022) Fedclassavg: Local representation learning for personalized federated learning on heterogeneous neural networks. In: Proceedings of the 51st International Conference on Parallel Processing, pp 1\u201310","DOI":"10.1145\/3545008.3545073"},{"issue":"4","key":"7728_CR35","doi-asserted-by":"publisher","first-page":"4108","DOI":"10.1109\/TIE.2023.3273272","volume":"71","author":"Y Yu","year":"2023","unstructured":"Yu Y, Guo L, Gao H, He Y, You Z, Duan A (2023) Fedcae: a new federated learning framework for edge-cloud collaboration based machine fault diagnosis. IEEE Trans Industr Electron 71(4):4108\u20134119","journal-title":"IEEE Trans Industr Electron"},{"issue":"10","key":"7728_CR36","doi-asserted-by":"publisher","first-page":"3191","DOI":"10.1109\/JSAC.2023.3310046","volume":"41","author":"X Zhou","year":"2023","unstructured":"Zhou X, Zheng X, Cui X, Shi J, Liang W, Yan Z, Yang LT, Shimizu S, Kevin I, Wang K (2023) Digital twin enhanced federated reinforcement learning with lightweight knowledge distillation in mobile networks. IEEE J Sel Areas Commun 41(10):3191\u20133211","journal-title":"IEEE J Sel Areas Commun"},{"issue":"3","key":"7728_CR37","doi-asserted-by":"publisher","first-page":"1181","DOI":"10.1109\/TFUZZ.2023.3319663","volume":"32","author":"H Li","year":"2023","unstructured":"Li H, Wang J (2023) From soft clustering to hard clustering: a collaborative annealing fuzzy $$c$$-means algorithm. IEEE Trans Fuzzy Syst 32(3):1181\u20131194","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"3","key":"7728_CR38","doi-asserted-by":"publisher","first-page":"442","DOI":"10.1137\/1025116","volume":"25","author":"W Peizhuang","year":"1983","unstructured":"Peizhuang W (1983) Pattern recognition with fuzzy objective function algorithms (james c. bezdek). SIAM Rev 25(3):442","journal-title":"SIAM Rev"},{"issue":"20","key":"7728_CR39","doi-asserted-by":"publisher","first-page":"20243","DOI":"10.1109\/JIOT.2022.3175149","volume":"9","author":"P Tian","year":"2022","unstructured":"Tian P, Liao W, Yu W, Blasch E (2022) Wscc: a weight-similarity-based client clustering approach for non-iid federated learning. IEEE Internet Things J 9(20):20243\u201320256","journal-title":"IEEE Internet Things J"},{"key":"7728_CR40","unstructured":"Hinton G (2015) Distilling the knowledge in a neural network. arXiv preprint arXiv:1503.02531"},{"key":"7728_CR41","unstructured":"Krizhevsky A, Nair V, Hinton G (2014) The CIFAR-10 Dataset. http:\/\/www.cs.toronto.edu\/kriz\/cifar.html. [Online]"},{"key":"7728_CR42","unstructured":"Netzer Y, Wang T, Coates A, Bissacco A, Wu B, Ng AY (2011) Reading digits in natural images with unsupervised feature learning. In: NIPS Workshop on Deep Learning and Unsupervised Feature Learning, vol 2011, p 4 . Granada"},{"key":"7728_CR43","unstructured":"Xiao H, Rasul K, Vollgraf R (2017) Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms. arXiv preprint arXiv:1708.07747"},{"key":"7728_CR44","doi-asserted-by":"crossref","unstructured":"Li Q, Diao Y, Chen Q, He B (2022) Federated learning on non-iid data silos: an experimental study. In: 2022 IEEE 38th International Conference on Data Engineering (ICDE), pp 965\u2013978 . IEEE","DOI":"10.1109\/ICDE53745.2022.00077"},{"key":"7728_CR45","unstructured":"Hsu T-MH, Qi H, Brown M (2019) Measuring the effects of non-identical data distribution for federated visual classification. arXiv preprint arXiv:1909.06335"}],"container-title":["The Journal of Supercomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-025-07728-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11227-025-07728-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-025-07728-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T16:22:04Z","timestamp":1757348524000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11227-025-07728-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,8]]},"references-count":45,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2025,9]]}},"alternative-id":["7728"],"URL":"https:\/\/doi.org\/10.1007\/s11227-025-07728-3","relation":{},"ISSN":["1573-0484"],"issn-type":[{"value":"1573-0484","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,8]]},"assertion":[{"value":"30 July 2025","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 September 2025","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"1318"}}