# Geometric Data Perturbation with Noisy-Anchor Alignment for Privacy-Preserving Collaborative Learning

arXiv: https://arxiv.org/abs/2608.18749 · HTML: https://mlsanity.com/paper/2608.18749/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 35 references that are in the map.
- First posted on arXiv 19 Aug 2026.

## Builds on (most cited first, 19 of 19)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [VGGFace2: A dataset for recognising faces across pose and age](https://mlsanity.com/paper/1710.08092/) (2017)
- [Towards Federated Learning at Scale: System Design](https://mlsanity.com/paper/1902.01046/) (2019)
- [Learning Face Representation from Scratch](https://mlsanity.com/paper/1411.7923/) (2014)
- [Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising](https://mlsanity.com/paper/1805.06530/) (2018)
- [Privacy-Preserving Machine Learning: Methods, Challenges and Directions](https://mlsanity.com/paper/2108.04417/) (2021)
- [MAAD-Face: A Massively Annotated Attribute Dataset for Face Images](https://mlsanity.com/paper/2012.01030/) (2020)
- [Selective Knowledge Sharing for Privacy-Preserving Federated Distillation without A Good Teacher](https://mlsanity.com/paper/2304.01731/) (2023)
- [Accuracy and Privacy Evaluations of Collaborative Data Analysis](https://mlsanity.com/paper/2101.11144/) (2021)
- [Non-readily identifiable data collaboration analysis for multiple datasets including personal information](https://mlsanity.com/paper/2208.14611/) (2022)
- [Near-Optimal Bounds for Generalized Orthogonal Procrustes Problem via Generalized Power Method](https://mlsanity.com/paper/2112.13725/) (2021)
- [On Lightweight Privacy-Preserving Collaborative Learning for Internet of Things by Independent Random Projections](https://mlsanity.com/paper/2012.07626/) (2020)
- [New Solutions Based on the Generalized Eigenvalue Problem for the Data Collaboration Analysis](https://mlsanity.com/paper/2404.14164/) (2024)
- [Data Collaboration Analysis with Orthonormal Basis Selection and Alignment](https://mlsanity.com/paper/2403.02780/) (2024)
- [Single-Round Clustered Federated Learning via Data Collaboration Analysis for Non-IID Data](https://mlsanity.com/paper/2601.09304/) (2026)
- [Nonlinear Data Integration via Kernel Methods for Data Collaboration Analysis](https://mlsanity.com/paper/2605.27219/) (2026)

## Abstract (arXiv)

Geometric data perturbation enables one-shot representation sharing for privacy-preserving collaborative learning: each participant applies a secret distance-preserving transformation to its private data and uploads the resulting representation to a central analyst. We study analyst-participant collusion, in which a colluding participant discloses its data and transformation to help the analyst reconstruct another participant's data. Independent participant-specific transformations block direct inversion through a disclosed common transformation but leave uploads in incompatible coordinate systems, degrading pooled learning. Data Collaboration analysis restores compatibility by aligning transformed copies of a common anchor matrix withheld from the analyst. We show that, when the centered anchor matrix has full column rank, a colluder who discloses it enables exact recovery of every participant's transformation and inversion of noiseless private representations. Adding noise to private-data representations leaves this transformation-recovery channel intact and reduces leakage at a substantial utility cost. Instead, we perturb the anchor representations: each participant perturbs only its transformed anchor representation, preserving the geometry of its private-data upload while turning known-anchor transformation recovery into a noisy estimation problem. The analyst estimates the alignment using a spectral estimator for a generalized orthogonal Procrustes problem. We analyze recovery attacks against this protocol and compare both noise placements on the CelebA and VGGFace2 facial image datasets. Under the evaluated collusion attacks, noisy-anchor alignment retains higher downstream accuracy at low identity-linkage levels. Participant-count experiments examine the utility gains and limitations of larger collaborations at comparable measured linkage.