Privacy in manifolds: Combining k-anonymity with differential privacy on Fréchet means

Abstract

While anonymization techniques have improved greatly in allowing data to be used again, it is still really hard to get useful information from anonymized data without risking people’s privacy. Conventional approaches such as k-Anonymity and Differential Privacy have limitations in preserving data utility and privacy simultaneously, particularly in high-dimensional spaces with manifold structures. We address this challenge by focusing on anonymizing data existing within high-dimensional spaces possessing manifold structures. To tackle these issues, we propose and implement a hybrid anonymization scheme termed as the ($\beta$, $k$, $b$)-anonymization method that combines elements of both differential privacy and k-anonymity. This approach aims to produce high-quality anonymized data that closely resembles real data in terms of knowledge extraction while safeguarding privacy. The Fréchet mean, an operation applicable in metric spaces and meaningful in the manifold setting, serves as a key aspect of our approach. It provides insight into the geometry of data points within high-dimensional spaces. Our goal is to anonymize this Fréchet mean using our proposed approach and minimize the distance between the original and anonymized Fréchet mean to achieve data privacy without significant loss of information. Additionally, we introduce a novel Fréchet mean clustering model designed to enhance the clustering process for high-dimensional spaces. Through theoretical analysis and practical experiments, we demonstrate that our approach outperforms traditional privacy models both in terms of preserving data utility and privacy. This research contributes to advancing privacy-preserving techniques for complex and non-linear data structures, ensuring a balance between data utility and privacy protection.