Privacy-Preserving Joint Distribution Analysis for Set-Valued Data via Local Differential Privacy

Set-valued data, an important data form expressing diversity and uncertainty, is widely used in fields such as recommendation systems and social network analysis. However, such data often contains fine-grained records, which may lead to the leakage of users’ sensitive information. To this end, some privacy-preserving set-valued data analysis schemes have been proposed. This paper first proposes a joint shift inference attack against the cyclic shift-based local differential privacy (LDP) protocol introduced by Huang et al. (10.1109/TIFS.2024.3423657), it exploits deterministic cyclic-shift patterns and significant frequency differences to infer the user’s original data. Experimental results demonstrate that the user’s original data can be inferred with a probability exceeding 96%. Theoretically, the cyclic-shift mechanism violates the core requirement of local differential privacy due to its non-surjective output space. To overcome the limitations of existing schemes, we propose a privacy-preserving joint distribution analysis scheme for set-valued data via LDP (SVJDA). It employs the Sparse Vector Mean Estimation (SVME) mechanism and utilizes a sign-based hashing function to compress data, allowing privacy-preserving joint distribution analysis while introducing only minimal additional noise. Theoretical analysis shows that SVJDA satisfies ϵ-LDP with minimal estimation error. The experimental results confirm that SVJDA achieves higher accuracy in joint distribution estimation while ensuring the accuracy of frequent itemset identification. For ϵ ∈ [0.4, 1], the L∞ error of SVJDA is only 7.208%–21.725% of SVSM and 2.821%–7.279% of LDP-RM, while its MSE is 0.00364%–2.338% of SVSM and 0.017%–0.068% of LDP-RM, demonstrating its superior performance.