Optimized Sparse Vector Aggregation Under Local Differential Privacy
Ellen Z. Zhang, Yunguo Guan, Rongxing Lu, Harry Zhang · IEEE Transactions on Information Forensics and Security · 2025
In crowdsourcing applications, gathering and analyzing users’ strong positive (1) or negative (-1) reactions to a large number of items is crucial for improving service quality, particularly in recommendation systems. However, protecting users’ privacy while handling diverse sparse patterns in contexts with a large dimension sizedposes significant challenges for efficient and privacy-preserving data aggregation. To address these challenges, in this paper, we propose an optimizedk-sparse vector mean estimation scheme under Local Differential Privacy (LDP), ensuring that each user’s entire set of up tokprivate values from {−1, 1} satisfies ε-LDP. Specifically, our proposed scheme employs a seed mining technique in conjunction with PRNG Randomizer, which allows users to send their data only once while enabling the server to accurately estimate any value’s mean in the domain. Our scheme achieves an asymptotically optimal error ofO( 1/ε√n), equivalent to that of a 1-sparse case, while also ensuring efficient communication costs. The communication cost remains at a minimal level ofO(1) (only 2 bytes per user’s report) for smallerkvalues and scales toO(k) for largerk, due to efficient binning strategies. Extensive experimental results confirm that our results align with theoretical expectations, demonstrating that our scheme not only preserves user privacy but also ensures higher accuracy compared to other schemes.