[2403.02780] Data Collaboration Analysis with Orthonormal Basis Selection and Alignment Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2403.02780 (cs) [Submitted on 5 Mar 2024 ( v1 ), last revised 22 Apr 2026 (this version, v9)] Title: Data Collaboration Analysis with Orthonormal Basis Selection and Alignment Authors: Keiyu Nosaka , Yamato Suetake , Yuichi Takano , Akiko Yoshise View a PDF of the paper titled Data Collaboration Analysis with Orthonormal Basis Selection and Alignment, by Keiyu Nosaka and 3 other authors View PDF HTML (experimental) Abstract: Data Collaboration (DC) enables multiple parties to jointly train a model by sharing only linear projections of their private datasets. The core challenge in DC is to align the bases of these projections without revealing each party's secret basis. While existing theory suggests that any target basis spanning the common subspace should suffice, in practice, the choice of basis can substantially affect both accuracy and numerical stability. We introduce Orthonormal Data Collaboration (ODC), which enforces orthonormal secret and target bases, thereby reducing alignment to the classical Orthogonal Procrustes problem, which admits a closed-form solution. We prove that the resulting change-of-basis matrices achieve orthogonal concordance, aligning all parties' representations up to a shared orthogonal transform and rendering downstream performance invariant to the target basis. Computationally, ODC reduces the alignment complexity from O(min{a(cl)^2,a^2cl}) to O(acl^2), and empirical evaluations show up to 100 times speedups with equal or better accuracy across benchmarks. ODC preserves DC's one-round communication pattern and privacy assumptions, providing a simple and efficient drop-in improvement to existing DC pipelines. Comments: 44 pages Subjects: Machine Learning (cs.LG) ; Optimization and Control (math.OC) Cite as: arXiv:2403.02780 [cs.LG] (or arXiv:2403.02780v9 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2403.02780 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Computers and Electrical Engineering, Volume 135, 2026, 111192 Related DOI : https://doi.org/10.1016/j.compeleceng.2026.111192 Focus to learn more DOI(s) linking to related resources Submission history From: Akiko Yoshise [ view email ] [v1] Tue, 5 Mar 2024 08:52:16 UTC (384 KB) [v2] Sun, 15 Dec 2024 03:50:07 UTC (1,536 KB) [v3] Tue, 17 Dec 2024 07:23:04 UTC (1,536 KB) [v4] Wed, 5 Feb 2025 01:33:52 UTC (1,034 KB) [v5] Fri, 8 Aug 2025 10:55:06 UTC (1,448 KB) [v6] Mon, 15 Dec 2025 06:06:06 UTC (1,649 KB) [v7] Thu, 5 Mar 2026 07:36:00 UTC (1,672 KB) [v8] Wed, 15 Apr 2026 11:36:15 UTC (1,672 KB) [v9] Wed, 22 Apr 2026 07:55:01 UTC (1,672 KB) Full-text links: Access Paper: View a PDF of the paper titled Data Collaboration Analysis with Orthonormal Basis Selection and Alignment, by Keiyu Nosaka and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2024-03 Change to browse by: cs math math.OC References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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