# Data Collaboration Analysis with Orthonormal Basis Selection and Alignment

arXiv: https://arxiv.org/abs/2403.02780 · HTML: https://mlsanity.com/paper/2403.02780/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 79 references that are in the map.
- First posted on arXiv 5 Mar 2024.

## Builds on (most cited first, 30 of 30)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [VGGFace2: A dataset for recognising faces across pose and age](https://mlsanity.com/paper/1710.08092/) (2017)
- [Federated Learning with Differential Privacy: Algorithms and Performance Analysis](https://mlsanity.com/paper/1911.00222/) (2019)
- [A Survey on Federated Learning Systems: Vision, Hype and Reality for Data Privacy and Protection](https://mlsanity.com/paper/1907.09693/) (2019)
- [Membership Inference Attacks on Machine Learning: A Survey](https://mlsanity.com/paper/2103.07853/) (2021)
- [Therapeutics Data Commons: Machine Learning Datasets and Tasks for Drug Discovery and Development](https://mlsanity.com/paper/2102.09548/) (2021)
- [Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising](https://mlsanity.com/paper/1805.06530/) (2018)
- [Applied Federated Learning: Improving Google Keyboard Query Suggestions](https://mlsanity.com/paper/1812.02903/) (2018)
- [Unsupervised Alignment of Embeddings with Wasserstein Procrustes](https://mlsanity.com/paper/1805.11222/) (2018)
- [Privacy-Preserving Machine Learning: Methods, Challenges and Directions](https://mlsanity.com/paper/2108.04417/) (2021)
- [DeepSecure: Scalable Provably-Secure Deep Learning](https://mlsanity.com/paper/1705.08963/) (2017)
- [Interpretable collaborative data analysis on distributed data](https://mlsanity.com/paper/2011.04437/) (2020)
- [Accuracy and Privacy Evaluations of Collaborative Data Analysis](https://mlsanity.com/paper/2101.11144/) (2021)
- [Differentially Private Federated Learning via Inexact ADMM](https://mlsanity.com/paper/2106.06127/) (2021)
- [Highly Efficient Knowledge Graph Embedding Learning with Orthogonal Procrustes Analysis](https://mlsanity.com/paper/2104.04676/) (2021)
- [Collaborative causal inference on distributed data](https://mlsanity.com/paper/2208.07898/) (2022)
- [Another Use of SMOTE for Interpretable Data Collaboration Analysis](https://mlsanity.com/paper/2208.12458/) (2022)
- [Non-readily identifiable data collaboration analysis for multiple datasets including personal information](https://mlsanity.com/paper/2208.14611/) (2022)
- [AutoGAN-based Dimension Reduction for Privacy Preservation](https://mlsanity.com/paper/1902.10799/) (2019)
- [Near-Optimal Bounds for Generalized Orthogonal Procrustes Problem via Generalized Power Method](https://mlsanity.com/paper/2112.13725/) (2021)
- [Report: State of the Art Solutions for Privacy Preserving Machine Learning in the Medical Context](https://mlsanity.com/paper/2201.11406/) (2022)
- [Data Collaboration Analysis applied to Compound Datasets and the Introduction of Projection data to Non-IID settings](https://mlsanity.com/paper/2308.00280/) (2023)

## Built on by (most cited first, 2 of 2)

- [Nonlinear Data Integration via Kernel Methods for Data Collaboration Analysis](https://mlsanity.com/paper/2605.27219/) (2026)
- [Geometric Data Perturbation with Noisy-Anchor Alignment for Privacy-Preserving Collaborative Learning](https://mlsanity.com/paper/2608.18749/) (2026)

## Abstract (arXiv)

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.