{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T04:50:43Z","timestamp":1783572643041,"version":"3.55.0"},"reference-count":38,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,12,16]],"date-time":"2024-12-16T00:00:00Z","timestamp":1734307200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["92367302"],"award-info":[{"award-number":["92367302"]}],"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":["201300210400"],"award-info":[{"award-number":["201300210400"]}],"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":["212102210094"],"award-info":[{"award-number":["212102210094"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Major Science and Technology Special Project of Henan Province","award":["92367302"],"award-info":[{"award-number":["92367302"]}]},{"name":"Major Science and Technology Special Project of Henan Province","award":["201300210400"],"award-info":[{"award-number":["201300210400"]}]},{"name":"Major Science and Technology Special Project of Henan Province","award":["212102210094"],"award-info":[{"award-number":["212102210094"]}]},{"name":"Key R&amp;D and Promotion Special Project of Henan Province","award":["92367302"],"award-info":[{"award-number":["92367302"]}]},{"name":"Key R&amp;D and Promotion Special Project of Henan Province","award":["201300210400"],"award-info":[{"award-number":["201300210400"]}]},{"name":"Key R&amp;D and Promotion Special Project of Henan Province","award":["212102210094"],"award-info":[{"award-number":["212102210094"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Federated learning enables devices to train models collaboratively while protecting data privacy. However, the computing power, memory, and communication capabilities of IoT devices are limited, making it difficult to train large-scale models on these devices. To train large models on resource-constrained devices, federated split learning allows for parallel training of multiple devices by dividing the model into different devices. However, under this framework, the client is heavily dependent on the server\u2019s computing resources, and a large number of model parameters must be transmitted during communication, which leads to low training efficiency. In addition, due to the heterogeneous distribution among clients, it is difficult for the trained global model to apply to all clients. To address these challenges, this paper designs a sparse gradient collaborative federated learning model for heterogeneous data on resource-constrained devices. First, the sparse gradient strategy is designed by introducing the position Mask to reduce the traffic. To minimize accuracy loss, the dequantization strategy is applied to restore the original dense gradient tensor. Second, the influence of each client on the global model is measured by Euclidean distance, and based on this, the aggregation weight is assigned to each client, and an adaptive weight strategy is developed. Finally, the sparse gradient quantization method is combined with an adaptive weighting strategy, and a collaborative federated learning algorithm is designed for heterogeneous data distribution. Extensive experiments demonstrate that the proposed algorithm achieves high classification efficiency, effectively addressing the challenges posed by data heterogeneity.<\/jats:p>","DOI":"10.3390\/e26121099","type":"journal-article","created":{"date-parts":[[2024,12,16]],"date-time":"2024-12-16T04:14:52Z","timestamp":1734322492000},"page":"1099","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Federated Collaborative Learning with Sparse Gradients for Heterogeneous Data on Resource-Constrained Devices"],"prefix":"10.3390","volume":"26","author":[{"given":"Mengmeng","family":"Li","sequence":"first","affiliation":[{"name":"College of Computer and Information Engineering, Henan University, Kaifeng 475001, China"},{"name":"Henan International Joint Laboratory of Intelligent Network Theory and Key Technology, Henan University, Kaifeng 475001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0755-0964","authenticated-orcid":false,"given":"Xin","family":"He","sequence":"additional","affiliation":[{"name":"Henan International Joint Laboratory of Intelligent Network Theory and Key Technology, Henan University, Kaifeng 475001, China"},{"name":"College of Software, Henan University, Kaifeng 475001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jinhua","family":"Chen","sequence":"additional","affiliation":[{"name":"Henan International Joint Laboratory of Intelligent Network Theory and Key Technology, Henan University, Kaifeng 475001, China"},{"name":"College of Software, Henan University, Kaifeng 475001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"15587","DOI":"10.1109\/JIOT.2024.3350241","article-title":"FedSL: A communication-efficient federated learning with split layer aggregation","volume":"11","author":"Zhang","year":"2024","journal-title":"IEEE Internet Things J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.future.2024.03.020","article-title":"PPSFL: Privacy-preserving split federated learning for heterogeneous data in edge-based internet of things","volume":"156","author":"Zheng","year":"2024","journal-title":"Future Gener. 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