{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T11:10:58Z","timestamp":1778152258256,"version":"3.51.4"},"publisher-location":"Cham","reference-count":29,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032253132","type":"print"},{"value":"9783032253149","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"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":[],"published-print":{"date-parts":[[2026]]},"DOI":"10.1007\/978-3-032-25314-9_23","type":"book-chapter","created":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T10:18:33Z","timestamp":1778149113000},"page":"323-336","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Breaking Down the\u00a0Radon Machine: The Geometry of\u00a0a\u00a0Robust Aggregation Scheme"],"prefix":"10.1007","author":[{"given":"Peter","family":"Blohm","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Patrick","family":"Indri","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thomas","family":"G\u00e4rtner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,5,8]]},"reference":[{"issue":"6","key":"23_CR1","doi-asserted-by":"publisher","first-page":"3452","DOI":"10.1109\/TCOMM.2020.2979149","volume":"68","author":"F Ang","year":"2020","unstructured":"Ang, F., Chen, L., Zhao, N., Chen, Y., Wang, W., Yu, F.R.: Robust federated learning with noisy communication. IEEE Trans. Commun. 68(6), 3452\u20133464 (2020). https:\/\/doi.org\/10.1109\/TCOMM.2020.2979149","journal-title":"IEEE Trans. Commun."},{"issue":"1","key":"23_CR2","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1007\/BF01589439","volume":"35","author":"RH Byrd","year":"1986","unstructured":"Byrd, R.H., Schnabel, R.B.: Continuity of the null space basis and constrained optimization. Math. Program. 35(1), 32\u201341 (1986). https:\/\/doi.org\/10.1007\/BF01589439","journal-title":"Math. Program."},{"key":"23_CR3","doi-asserted-by":"crossref","unstructured":"Cao, X., Fang, M., Liu, J., Gong, N.Z.: FLTrust: byzantine-robust Federated Learning via Trust Bootstrapping. In: ISOC Network and Distributed System Security Symposium (NDSS) (2021)","DOI":"10.14722\/ndss.2021.24434"},{"key":"23_CR4","doi-asserted-by":"publisher","unstructured":"Clarkson, K.L., Eppstein, D., Miller, G.L., Sturtivant, C., Teng, S.H.: Approximating center points with iterated Radon points. In: Proceedings of the Ninth Annual Symposium on Computational Geometry, pp. 91\u201398 (1993). https:\/\/doi.org\/10.1145\/160985.161004","DOI":"10.1145\/160985.161004"},{"key":"23_CR5","doi-asserted-by":"publisher","unstructured":"Edelsbrunner, H.: Algorithms in Combinatorial Geometry. Monographs in Theoretical Computer Science. An EATCS Series, Springer, Heidelberg (1987). https:\/\/doi.org\/10.1007\/978-3-642-61568-9","DOI":"10.1007\/978-3-642-61568-9"},{"key":"23_CR6","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1007\/978-3-540-27819-1_38","volume-title":"Learning Theory","author":"R Gilad-Bachrach","year":"2004","unstructured":"Gilad-Bachrach, R., Navot, A., Tishby, N.: Bayes and Tukey meet at the center point. In: Shawe-Taylor, J., Singer, Y. (eds.) COLT 2004. LNCS (LNAI), vol. 3120, pp. 549\u2013563. Springer, Heidelberg (2004). https:\/\/doi.org\/10.1007\/978-3-540-27819-1_38"},{"key":"23_CR7","doi-asserted-by":"publisher","unstructured":"Hao, M., Li, H., Xu, G., Liu, S., Yang, H.: Towards efficient and privacy-preserving federated deep learning. In: ICC 2019 - 2019 IEEE International Conference on Communications (ICC) (2019). https:\/\/doi.org\/10.1109\/ICC.2019.8761267","DOI":"10.1109\/ICC.2019.8761267"},{"key":"23_CR8","doi-asserted-by":"publisher","unstructured":"Johnson, N.L., Kemp, A.W., Kotz, S.: Hypergeometric distributions. In: Shewhart, W.A., Wilks, S.S. (eds.) Univariate Discrete Distributions, pp. 455\u2013486. Wiley Series in Probability and Statistics. Wiley, New York (2005). https:\/\/doi.org\/10.1002\/0471715816.ch6","DOI":"10.1002\/0471715816.ch6"},{"key":"23_CR9","unstructured":"Kamp, M., Boley, M., Missura, O., G\u00e4rtner, T.: Effective parallelisation for machine learning. In: Guyon, I., et al. (eds.) Advances in Neural Information Processing Systems, vol.\u00a030. Curran Associates, Inc. (2017). https:\/\/proceedings.neurips.cc\/paper_files\/paper\/2017\/file\/38811c5285e34e2e3319ab7d9f2cfa5b-Paper.pdf"},{"key":"23_CR10","unstructured":"Kamp, M., Fischer, J., Vreeken, J.: Federated learning from small datasets. In: The Eleventh International Conference on Learning Representations (2023). https:\/\/openreview.net\/forum?id=hDDV1lsRV8"},{"key":"23_CR11","doi-asserted-by":"crossref","unstructured":"Lamport, L., Shostak, R., Pease, M.: The Byzantine Generals Problem, pp. 203\u2013226. Association for Computing Machinery, New York, NY, USA (2019). https:\/\/doi.org\/10.1145\/3335772.3335936","DOI":"10.1145\/3335772.3335936"},{"issue":"1","key":"23_CR12","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1186\/s42400-021-00105-6","volume":"5","author":"P Liu","year":"2022","unstructured":"Liu, P., Xu, X., Wang, W.: Threats, attacks and defenses to federated learning: issues, taxonomy and perspectives. Cybersecurity 5(1), 4 (2022). https:\/\/doi.org\/10.1186\/s42400-021-00105-6","journal-title":"Cybersecurity"},{"issue":"7","key":"23_CR13","doi-asserted-by":"publisher","first-page":"8726","DOI":"10.1109\/TNNLS.2022.3216981","volume":"35","author":"L Lyu","year":"2024","unstructured":"Lyu, L., et al.: Privacy and robustness in federated learning: attacks and defenses. IEEE Trans. Neural Netw. Learn. Syst. 35(7), 8726\u20138746 (2024). https:\/\/doi.org\/10.1109\/TNNLS.2022.3216981","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"4","key":"23_CR14","doi-asserted-by":"publisher","first-page":"2308","DOI":"10.3150\/14-BEJ645","volume":"21","author":"S Minsker","year":"2015","unstructured":"Minsker, S.: Geometric median and robust estimation in Banach spaces. Bernoulli 21(4), 2308\u20132335 (2015). https:\/\/doi.org\/10.3150\/14-BEJ645","journal-title":"Bernoulli"},{"issue":"9","key":"23_CR15","doi-asserted-by":"publisher","first-page":"949","DOI":"10.1080\/00029890.1972.11993165","volume":"79","author":"B Peterson","year":"1972","unstructured":"Peterson, B.: The geometry of Radon\u2019s theorem. Am. Math. Mon. 79(9), 949\u2013963 (1972). https:\/\/doi.org\/10.1080\/00029890.1972.11993165","journal-title":"Am. Math. Mon."},{"key":"23_CR16","doi-asserted-by":"publisher","unstructured":"Pillutla, K., Kakade, S.M., Harchaoui, Z.: Robust aggregation for federated learning. IEEE Trans. Sig. Process. 70, 1142\u20131154 (2022). https:\/\/doi.org\/10.1109\/TSP.2022.3153135","DOI":"10.1109\/TSP.2022.3153135"},{"key":"23_CR17","doi-asserted-by":"publisher","unstructured":"Radon, J.: Mengen konvexer K\u00f6rper, die einen gemeinsamen Punkt enthalten. Mathematische Annalen 83(1\u20132) (1921). https:\/\/doi.org\/10.1007\/BF01464231","DOI":"10.1007\/BF01464231"},{"issue":"1","key":"23_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41746-020-00323-1","volume":"3","author":"N Rieke","year":"2020","unstructured":"Rieke, N., et al.: The future of digital health with federated learning. NPJ Digit. Med. 3(1), 1\u20137 (2020). https:\/\/doi.org\/10.1038\/s41746-020-00323-1","journal-title":"NPJ Digit. Med."},{"key":"23_CR19","doi-asserted-by":"publisher","unstructured":"Shamir, O., Srebro, N.: Distributed stochastic optimization and learning. In: 2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton) (2014). https:\/\/doi.org\/10.1109\/ALLERTON.2014.7028543","DOI":"10.1109\/ALLERTON.2014.7028543"},{"key":"23_CR20","doi-asserted-by":"publisher","unstructured":"Uzilov, A.V., Keegan, J.M., Mathews, D.H.: Detection of non-coding RNAs on the basis of predicted secondary structure formation free energy change. BMC Bioinform. 7, 1\u201330 (2006). https:\/\/doi.org\/10.1186\/1471-2105-7-173","DOI":"10.1186\/1471-2105-7-173"},{"issue":"2","key":"23_CR21","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1145\/2641190.2641198","volume":"15","author":"J Vanschoren","year":"2013","unstructured":"Vanschoren, J., van Rijn, J.N., Bischl, B., Torgo, L.: OpenML: networked science in machine learning. SIGKDD Explor. 15(2), 49\u201360 (2013). https:\/\/doi.org\/10.1145\/2641190.2641198","journal-title":"SIGKDD Explor."},{"key":"23_CR22","doi-asserted-by":"publisher","unstructured":"Verbraeken, J., Wolting, M., Katzy, J., Kloppenburg, J., Verbelen, T., Rellermeyer, J.S.: A survey on distributed machine learning. ACM Comput. Surv. 53(2) (2020). https:\/\/doi.org\/10.1145\/3377454","DOI":"10.1145\/3377454"},{"key":"23_CR23","doi-asserted-by":"publisher","unstructured":"Wei, K., et al.: Federated learning with differential privacy: algorithms and performance analysis. IEEE Trans. Inf. Forensics Secur. 15, 3454\u20133469 (2020). https:\/\/doi.org\/10.1109\/TIFS.2020.2988575","DOI":"10.1109\/TIFS.2020.2988575"},{"key":"23_CR24","doi-asserted-by":"publisher","unstructured":"Whiteson, D.: SUSY. UCI Machine Learning Repository (2014). https:\/\/doi.org\/10.24432\/C54606","DOI":"10.24432\/C54606"},{"key":"23_CR25","unstructured":"Xing, Z., Zhang, Z., Liu, J., Zhang, Z., Li, M., Zhu, L., Russello, G.: Zero-Knowledge Proof Meets Machine Learning in Verifiability: A Survey (2023). https:\/\/arxiv.org\/abs\/2310.14848"},{"key":"23_CR26","volume-title":"Geometry and Symmetry","author":"PB Yale","year":"1988","unstructured":"Yale, P.B.: Geometry and Symmetry. Dover Publications, New York (1988)"},{"key":"23_CR27","doi-asserted-by":"publisher","unstructured":"Yang, Q., Liu, Y., Chen, T., Tong, Y.: Federated machine learning: concept and applications. ACM Trans. Intell. Syst. Technol. 10(2) (2019). https:\/\/doi.org\/10.1145\/3298981","DOI":"10.1145\/3298981"},{"key":"23_CR28","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.: A survey on federated learning. Knowl.-Based Syst. 216, 106775 (2021). https:\/\/doi.org\/10.1016\/j.knosys.2021.106775","journal-title":"Knowl.-Based Syst."},{"key":"23_CR29","doi-asserted-by":"publisher","DOI":"10.1145\/3678181","author":"Y Zhang","year":"2024","unstructured":"Zhang, Y., et al.: A survey of trustworthy federated learning: issues, solutions, and challenges. ACM Trans. Intell. Syst. Technol. (2024). https:\/\/doi.org\/10.1145\/3678181","journal-title":"ACM Trans. Intell. Syst. Technol."}],"container-title":["Communications in Computer and Information Science","Machine Learning and Principles and Practice of Knowledge Discovery in Databases"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-25314-9_23","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T10:18:40Z","timestamp":1778149120000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-25314-9_23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"ISBN":["9783032253132","9783032253149"],"references-count":29,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-25314-9_23","relation":{},"ISSN":["1865-0929","1865-0937"],"issn-type":[{"value":"1865-0929","type":"print"},{"value":"1865-0937","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]},"assertion":[{"value":"8 May 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"The authors have no competing interests to declare that are relevant to the content of this article.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Disclosure of Interests"}},{"value":"ECML PKDD","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Joint European Conference on Machine Learning and Knowledge Discovery in Databases","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Vilnius","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Lithuania","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"8 September 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"12 September 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"24","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ecml2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/2024.ecmlpkdd.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}