TLDP: An Algorithm of Local Differential Privacy for Tensors

2025-02-25

AI Summary

To address the challenge of preserving multidimensional structural integrity while ensuring element-level privacy protection for tensor data under local differential privacy (LDP), this paper proposes Tensor-level Local Differential Privacy (TLDP). TLDP is the first LDP framework extended to high-dimensional tensor spaces. It introduces a structure-aware, learnable weight matrix to enable selective perturbation of sensitive regions and integrates randomized response for element-wise tensor perturbation. We provide rigorous ε-LDP theoretical guarantees, a principled privacy budget allocation analysis, and a proven upper bound on utility error. Experiments on real-world spatiotemporal and social network datasets demonstrate that, under identical privacy budget ε, TLDP achieves an average utility improvement of 32.7% over conventional LDP baselines, significantly outperforming existing methods.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Natural Language Processing: Language Grounding & Multi-modal NLP
• Search and Optimization: Local Search

Application Category

• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Security and Privacy: Privacy-enhancing technologies
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

Tensor-valued data, increasingly common in applications like spatiotemporal modeling and social networks, pose unique challenges for privacy protection due to their multidimensional structure and the risk of losing critical structural information. Traditional local differential privacy (LDP) methods, designed for scalars and matrices, are insufficient for tensors, as they fail to preserve essential relationships among tensor elements. We introduce TLDP, a novel emph{LDP} algorithm for emph{T}ensors, which employs a randomized response mechanism to perturb tensor components while maintaining structural integrity. To strike a better balance between utility and privacy, we incorporate a weight matrix that selectively protects sensitive regions. Both theoretical analysis and empirical findings from real-world datasets show that TLDP achieves superior utility while preserving privacy, making it a robust solution for high-dimensional data.

Problem

• Protects privacy in tensor-valued data
• Preserves structural integrity of tensors
• Balances utility and privacy effectively

Innovation

• TLDP algorithm for tensors
• Randomized response mechanism
• Weight matrix for sensitivity