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

Geometric Data Perturbation (GDP) enables one-shot, privacy-preserving collaborative learning: each participant applies a distance-preserving transformation to its private data and uploads only the resulting representation to a central analyst. We study GDP under analyst-participant collusion, in which the analyst combines all uploaded representations with the private data and transformations disclosed by colluding participants to recover a non-colluding participant's private data. Participant-specific independent transformations resist this attack but map participants' data into incompatible representation spaces, degrading downstream model performance. Shared-anchor alignment from Data Collaboration (DC) analysis restores compatibility and improves utility, but we show that disclosing the DC anchor matrix enables exact recovery of non-colluding participants' private data even in the presence of collusion. Adding noise directly to the private-data representations mitigates this vulnerability but substantially reduces utility. We propose adding noise to the anchor representations instead. Each participant independently transforms its private data and the shared anchor matrix, perturbs only the resulting anchor representation, and uploads both representations in a single round. Using the noisy anchor representations, the analyst aligns the private-data representations by solving a Generalized Orthogonal Procrustes Problem. We characterize alignment and recovery errors, specialize a conservative sufficient condition for convergence of the alignment to our setting, and analyze three recovery attacks. Experiments on MNIST and CelebA show that, across the evaluated attacks and deployment settings, anchor noise achieves higher learning accuracy than private-data noise at comparable measured leakage, yielding a more favorable privacy-utility trade-off under the specified collusion model.

Data Collaboration Analysis Over Matrix Manifolds

The effectiveness of machine learning (ML) algorithms is deeply intertwined with the quality and diversity of their training datasets. Improved datasets, marked by superior quality, enhance the predictive accuracy and broaden the applicability of models across varied scenarios. Researchers often integrate data from multiple sources to mitigate biases and limitations of single-source datasets. However, this extensive data amalgamation raises significant ethical concerns, particularly regarding user privacy and the risk of unauthorized data disclosure. Various global legislative frameworks have been established to address these privacy issues. While crucial for safeguarding privacy, these regulations can complicate the practical deployment of ML technologies. Privacy-Preserving Machine Learning (PPML) addresses this challenge by safeguarding sensitive information, from health records to geolocation data, while enabling the secure use of this data in developing robust ML models. Within this realm, the Non-Readily Identifiable Data Collaboration (NRI-DC) framework emerges as an innovative approach, potentially resolving the 'data island' issue among institutions through non-iterative communication and robust privacy protections. However, in its current state, the NRI-DC framework faces model performance instability due to theoretical unsteadiness in creating collaboration functions. This study establishes a rigorous theoretical foundation for these collaboration functions and introduces new formulations through optimization problems on matrix manifolds and efficient solutions. Empirical analyses demonstrate that the proposed approach, particularly the formulation over orthogonal matrix manifolds, significantly enhances performance, maintaining consistency and efficiency without compromising communication efficiency or privacy protections.