{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T06:58:22Z","timestamp":1764831502036,"version":"3.46.0"},"reference-count":43,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2025,12,2]],"date-time":"2025-12-02T00:00:00Z","timestamp":1764633600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Distributed cloud networks spanning multiple jurisdictions face significant challenges in anomaly detection due to privacy constraints, regulatory requirements, and communication limitations. This paper presents a mathematically rigorous framework for privacy-preserving federated learning on hierarchical graph neural networks, providing theoretical convergence guarantees and optimisation bounds for distributed anomaly detection. A novel layer-wise federated aggregation mechanism is introduced, featuring a proven convergence rate O1\/T. That preserves hierarchical structure during distributed training. The theoretical analysis establishes differential privacy guarantees of \u03b5=1.0,\u00a0\u03b4=10\u22125 through layer-specific noise calibration, achieving optimal privacy\u2013utility tradeoffs. The proposed optimisation framework incorporates: (1) convergence-guaranteed layer-wise aggregation with bounded gradient norms, (2) privacy-preserving mechanisms with formal composition analysis under the Moments Accountant framework, (3) meta-learning-based personalisation with theoretical generalisation bounds, and (4) communication-efficient protocols with a proven 93% reduction in overhead. Rigorous evaluation on the FEDGEN testbed, spanning 2780 km across Nigeria and the Democratic Republic of Congo, demonstrates superior performance with hierarchical F1-scores exceeding 95% across all regions, while maintaining theoretical guarantees. The framework\u2019s convergence analysis shows robustness under realistic constraints, including 67% client participation, 200 ms latency, and 20 Mbps bandwidth limitations. This work advances the theoretical foundations of federated graph learning while providing practical deployment guidelines for cross-jurisdictional cloud networks.<\/jats:p>","DOI":"10.3390\/computation13120283","type":"journal-article","created":{"date-parts":[[2025,12,2]],"date-time":"2025-12-02T15:31:17Z","timestamp":1764689477000},"page":"283","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Convergence Analysis and Optimisation of Privacy-Preserving Federated Learning for Hierarchical Graph Neural Networks in Distributed Cloud Anomaly Detection"],"prefix":"10.3390","volume":"13","author":[{"given":"Comfort","family":"Lawal","sequence":"first","affiliation":[{"name":"Department of Electrical and Information Engineering, College of Engineering, Covenant University, Ota 112212, Nigeria"},{"name":"Covenant Applied Informatics and Communication African Centre of Excellence, Covenant University, Ota 112212, Nigeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7349-7500","authenticated-orcid":false,"given":"Olatayo M.","family":"Olaniyan","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, Federal University Oye-Ekiti, Oye 370112, Nigeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7594-276X","authenticated-orcid":false,"given":"Kennedy","family":"Okokpujie","sequence":"additional","affiliation":[{"name":"Department of Electrical and Information Engineering, College of Engineering, Covenant University, Ota 112212, Nigeria"},{"name":"Covenant Applied Informatics and Communication African Centre of Excellence, Covenant University, Ota 112212, Nigeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9227-7389","authenticated-orcid":false,"given":"Emmanuel","family":"Adetiba","sequence":"additional","affiliation":[{"name":"Department of Electrical and Information Engineering, College of Engineering, Covenant University, Ota 112212, Nigeria"},{"name":"Covenant Applied Informatics and Communication African Centre of Excellence, Covenant University, Ota 112212, Nigeria"},{"name":"Honorary Research Associate, Institute for Systems Science, Durban University of Technology, Durban 4001, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/978-3-319-22168-7_4","article-title":"Cloud of things: Integration of IoT with cloud computing","volume":"Volume 36","author":"Aazam","year":"2016","journal-title":"Studies in Systems, Decision and Control"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1145\/1496091.1496100","article-title":"A break in the clouds: Towards a cloud definition","volume":"39","author":"Vaquero","year":"2009","journal-title":"ACM SIGCOMM Comput. Commun. Rev."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1109\/MCOM.2017.1600267CM","article-title":"Security and privacy in smart city applications: Challenges and solutions","volume":"55","author":"Zhang","year":"2017","journal-title":"IEEE Commun. Mag."},{"key":"ref_4","unstructured":"McMahan, B., and Ramage, D. (2025, July 18). Federated Learning: Collaborative Machine Learning Without Centralised Training Data. Google Research Blog, April 2017. Available online: https:\/\/research.google\/blog\/federated-learning-collaborative-machine-learning-without-centralized-training-data\/."},{"key":"ref_5","unstructured":"Pearson, S., and Benameur, A. (December, January 30). Privacy, security and trust issues arising from cloud computing. Proceedings of the 2nd IEEE International Conference Cloud Computing Technology and Science (CloudCom), Indianapolis, IN, USA."},{"key":"ref_6","unstructured":"European Parliament (2025, July 18). Regulation (EU) 2016\/679 of the European Parliament and of the Council of 27 April 2016 on the Protection of Natural Persons with Regard to the Processing of Personal Data and on the Free Movement of Such Data, and Repealing Directive 95\/46\/EC (General Data Protection Regulation) (Text with EEA Relevance). EUR-Lex, April 2016, Available online: https:\/\/eur-lex.europa.eu\/eli\/reg\/2016\/679\/oj\/eng."},{"key":"ref_7","unstructured":"Hsieh, K., Ananthanarayanan, G., Bodik, P., Venkataraman, S., and Stoica, I. (2017, January 27\u201329). Gaia: Geo-distributed machine learning approaching LAN speeds. Proceedings of the 14th USENIX Symposium on Networked Systems Design and Implementation, Boston, MA, USA."},{"key":"ref_8","unstructured":"Kone\u010dn\u00fd, J., McMahan, H.B., Yu, F.X., Richt\u00e1rik, P., Suresh, A.T., and Bacon, D. (2016, January 9). Federated learning: Strategies for improving communication efficiency. Proceedings of the NIPS Workshop on Private Multi-Party Machine Learning, Barcelona, Spain."},{"key":"ref_9","unstructured":"McMahan, H.B., Moore, E., Ramage, D., Hampson, S., and Arcas, B.A.Y. (2017, January 20\u201322). Communication-efficient learning of deep networks from decentralized data. Proceedings of the 20th International Conference Artificial Intelligence and Statistics (AISTATS), Fort Lauderdale, FL, USA."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Wu, C., Wu, F., Cao, Y., Huang, Y., and Xie, X. (2021). FedGNN: Federated graph neural network for privacy-preserving recommendation. arXiv.","DOI":"10.1038\/s41467-022-30714-9"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"100008","DOI":"10.1016\/j.hcc.2021.100008","article-title":"A survey of federated learning for edge computing: Research problems and solutions","volume":"1","author":"Xia","year":"2021","journal-title":"High Confid. Comput."},{"key":"ref_12","unstructured":"Shokri, R., and Shmatikov, V. (October, January 29). Privacy-preserving deep learning. Proceedings of the 53rd Annual Allerton Conference Communication, Control, and Computing (Allerton), Monticello, IL, USA."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"111023","DOI":"10.1016\/j.comnet.2024.111023","article-title":"A review of federated learning applications in intrusion detection systems","volume":"258","author":"Belenguer","year":"2025","journal-title":"Comput. Netw."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3339474","article-title":"Federated machine learning: Concept and applications","volume":"10","author":"Yang","year":"2019","journal-title":"ACM Trans. Intell. Syst. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"7751","DOI":"10.1109\/JIOT.2020.2991401","article-title":"Privacy-preserving traffic flow prediction: A federated learning approach","volume":"7","author":"Liu","year":"2020","journal-title":"IEEE Internet Things J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1205","DOI":"10.1109\/JSAC.2019.2904348","article-title":"Adaptive federated learning in resource constrained edge computing systems","volume":"37","author":"Wang","year":"2019","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1561\/2200000083","article-title":"Advances and open problems in federated learning","volume":"14","author":"Kairouz","year":"2021","journal-title":"Found. Trends Mach. Learn."},{"key":"ref_18","unstructured":"Hamilton, W.L., Ying, R., and Leskovec, J. (2017, January 4\u20139). Inductive representation learning on large graphs. Proceedings of the Advances in Neural Information Processing Systems 30 (NIPS 2017), Long Beach, CA, USA."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"e27","DOI":"10.1017\/dap.2024.19","article-title":"Overcoming intergovernmental data sharing challenges with federated learning","volume":"6","author":"Sprenkamp","year":"2024","journal-title":"Data Policy"},{"key":"ref_20","unstructured":"Xu, H., Pan, M., Huang, X., and Shen, A. (2025, July 18). Federated Learning in Autonomous Vehicles Using Cross-Jurisdictional Training. NVIDIA Technical Blog. Available online: https:\/\/developer.nvidia.com\/blog\/federated-learning-in-autonomous-vehicles-using-cross-jurisdictional-training\/."},{"key":"ref_21","unstructured":"Kipf, T.N., and Welling, M. (2017, January 24\u201326). Semi-supervised classification with graph convolutional networks. Proceedings of the 5th International Conference Learning Representations (ICLR), Toulon, France."},{"key":"ref_22","unstructured":"Zhang, K., Yang, C., Li, X., Sun, L., and Yiu, S.M. (2021). Subgraph federated learning with missing neighbor generation. arXiv."},{"key":"ref_23","unstructured":"He, C., Balasubramanian, K., Ceyani, E., Yang, C., Xie, H., Sun, L., He, L., Yang, L., Yu, P.S., and Rong, Y. (2021). FedGraphNN: A federated learning system and benchmark for graph neural networks. arXiv."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1155","DOI":"10.14778\/2732977.2732989","article-title":"Differentially private event sequences over infinite streams","volume":"7","author":"Kellaris","year":"2014","journal-title":"Proc. VLDB Endow."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Dwork, C., McSherry, F., Nissim, K., and Smith, A. (2006, January 4\u20137). Calibrating noise to sensitivity in private data analysis. Proceedings of the 3rd Theory of Cryptography Conference (TCC), New York, NY, USA.","DOI":"10.1007\/11681878_14"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3454","DOI":"10.1109\/TIFS.2020.2988575","article-title":"Federated learning with differential privacy: Algorithms and performance analysis","volume":"15","author":"Wei","year":"2020","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Truex, S., Baracaldo, N., Anwar, A., Steinke, T., Ludwig, H., Zhang, R., and Zhou, Y. (2019, January 15). A hybrid approach to privacy-preserving federated learning. Proceedings of the 12th ACM Workshop on Artificial Intelligence and Security (AISec), London, UK.","DOI":"10.1145\/3338501.3357370"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"12012","DOI":"10.1109\/TKDE.2021.3118815","article-title":"A comprehensive survey on graph anomaly detection with deep learning","volume":"35","author":"Ma","year":"2023","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"626","DOI":"10.1007\/s10618-014-0365-y","article-title":"Graph-based anomaly detection and description: A survey","volume":"29","author":"Akoglu","year":"2015","journal-title":"Data Min. Knowl. Discov."},{"key":"ref_30","unstructured":"Li, T., Sahu, A.K., Zaheer, M., Sanjabi, M., Talwalkar, A., and Smith, V. (2020, January 2\u20134). Federated optimization in heterogeneous networks. Proceedings of the Machine Learning and Systems 2 (MLSys), Austin, TX, USA. Available online: https:\/\/proceedings.mlsys.org\/paper_files\/paper\/2020\/file\/1f5fe83998a09396ebe6477d9475ba0c-Paper.pdf."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1561\/0400000042","article-title":"The algorithmic foundations of differential privacy","volume":"9","author":"Dwork","year":"2014","journal-title":"Found. Trends Theor. Comput. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Abadi, M., Chu, A., Goodfellow, I., McMahan, H.B., Mironov, I., Talwar, K., and Zhang, L. (2016, January 24\u201328). Deep learning with differential privacy. Proceedings of the 2016 ACM SIGSAC Conference Computer and Communications Security (CCS), Vienna, Austria.","DOI":"10.1145\/2976749.2978318"},{"key":"ref_33","unstructured":"Finn, C., Abbeel, P., and Levine, S. (2017, January 6\u201311). Model-agnostic meta-learning for fast adaptation of deep networks. Proceedings of the 34th International Conference Machine Learning (ICML), Sydney, Australia."},{"key":"ref_34","unstructured":"Zhao, Y., Li, M., Lai, L., Suda, N., Civin, D., and Chandra, V. (2018). Federated learning with non-IID data. arXiv."},{"key":"ref_35","unstructured":"Mohri, M., Sivek, G., and Suresh, A.T. (2019, January 10\u201315). Agnostic federated learning. Proceedings of the 36th International Conference Machine Learning (ICML), Long Beach, CA, USA."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1134","DOI":"10.1145\/1968.1972","article-title":"A theory of the learnable","volume":"27","author":"Valiant","year":"1984","journal-title":"Commun. ACM"},{"key":"ref_37","unstructured":"Fallah, A., Mokhtari, A., and Ozdaglar, A. (2020). Personalized federated learning: A meta-learning approach. arXiv."},{"key":"ref_38","unstructured":"Geiping, J., Bauermeister, H., Dr\u00f6ge, H., and Moeller, M. (2020, January 6\u201312). Inverting gradients\u2014How easy is it to break privacy in federated learning?. Proceedings of the Advances in Neural Information Processing Systems 33 (NeurIPS 2020), Virtual Conference. Available online: https:\/\/proceedings.neurips.cc\/paper\/2020\/hash\/c4ede56bbd98819ae6112b20ac6bf145-Abstract.html."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Nasr, M., Shokri, R., and Houmansadr, A. (2019, January 20\u201322). Comprehensive privacy analysis of deep learning: Passive and active white-box inference attacks against centralized and federated learning. Proceedings of the 2019 IEEE Symposium on Security and Privacy (SP), San Francisco, CA, USA.","DOI":"10.1109\/SP.2019.00065"},{"key":"ref_40","unstructured":"He, X., Jia, J., Backes, M., Gong, N.Z., and Zhang, Y. (2021, January 11\u201313). Stealing links from graph neural networks. Proceedings of the 30th USENIX Security Symposium, Virtual Conference. Available online: https:\/\/www.usenix.org\/conference\/usenixsecurity21\/presentation\/he-xinlei."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"101246","DOI":"10.1109\/ACCESS.2025.3577706","article-title":"SecFedMDM-1: A Federated Learning-Based Malware Detection Model for Interconnected Cloud Infrastructures","volume":"13","author":"Mughole","year":"2025","journal-title":"IEEE Access"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"4602","DOI":"10.11591\/ijece.v14i4.pp4602-4615","article-title":"Hybridization of the Q-learning and honey bee foraging algorithms for load balancing in cloud environments","volume":"14","author":"Adewale","year":"2024","journal-title":"Int. J. Electr. Comput. Eng."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Ewejobi, P., Okokpujie, K., Adetiba, E., and Alao, B. (2024, January 2\u20134). Homomorphic Encryption for Genomics Data Storage on a Federated Cloud: A Mini Review. Proceedings of the 2024 International Conference on Science, Engineering and Business for Driving Sustainable Development Goals (SEB4SDG), Omu-Aran, Nigeria.","DOI":"10.1109\/SEB4SDG60871.2024.10630232"}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/13\/12\/283\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T05:18:15Z","timestamp":1764825495000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/13\/12\/283"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,2]]},"references-count":43,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["computation13120283"],"URL":"https:\/\/doi.org\/10.3390\/computation13120283","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2025,12,2]]}}}