Mixture Distribution-Based Truth Discovery Algorithm under Local Differential Privacy

ZHANG Pengfei; AN Jianlong; CHENG Xiang; ZHANG Zhikun; SUN Li; ZHANG Ji; ZHU Yibo

doi:10.11999/JEIT240936

Volume 47 Issue 6

Jun. 2025

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ZHANG Pengfei, AN Jianlong, CHENG Xiang, ZHANG Zhikun, SUN Li, ZHANG Ji, ZHU Yibo. Mixture Distribution-Based Truth Discovery Algorithm under Local Differential Privacy[J]. Journal of Electronics & Information Technology, 2025, 47(6): 1896-1910. doi: 10.11999/JEIT240936

Citation:

ZHANG Pengfei, AN Jianlong, CHENG Xiang, ZHANG Zhikun, SUN Li, ZHANG Ji, ZHU Yibo. Mixture Distribution-Based Truth Discovery Algorithm under Local Differential Privacy[J]. Journal of Electronics & Information Technology, 2025, 47(6): 1896-1910. doi: 10.11999/JEIT240936

Citation:

ZHANG Pengfei, AN Jianlong, CHENG Xiang, ZHANG Zhikun, SUN Li, ZHANG Ji, ZHU Yibo. Mixture Distribution-Based Truth Discovery Algorithm under Local Differential Privacy[J]. Journal of Electronics & Information Technology, 2025, 47(6): 1896-1910. doi: 10.11999/JEIT240936

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Mixture Distribution-Based Truth Discovery Algorithm under Local Differential Privacy

doi: 10.11999/JEIT240936 cstr: 32379.14.JEIT240936

ZHANG Pengfei^{1, 2},
AN Jianlong¹,
CHENG Xiang^{3, 4},
ZHANG Zhikun^{5
,
,},
SUN Li⁶,
ZHANG Ji⁷,
ZHU Yibo¹

1.
School of Computer Science and Engineering, Anhui University of Science and Technology, Huainan 232001, China
2.
Key Laboratory of Service Computing, Yunnan University of Finance and Economics, Kunming 650221, China
3.
National Pilot Software Engineering School, Beijing University of Posts and Telecommunications, Beijing 100876, China
4.
Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China
5.
College of Computer Science and Technology, Zhejiang University, Hangzhou 310058, China
6.
School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China
7.
School of Mathematics, Physics and Computing, University of Southern Queensland Australia, Toowoomba 4350, Australia

Funds: The Scientific Research Start-up Foundation for High-level Talents of Anhui University of Science and Technology (2023yjrc92), The Foundation of Yunnan Key Laboratory of Service Computing (YNSC24116), The National Natural Science Foundation of China (62202164)

Received Date: 2024-10-25
Rev Recd Date: 2025-02-27

Available Online: 2025-03-14

Publish Date: 2025-06-30

Abstract

Abstract

Objective Mobile crowd sensing is recognized as one of the significant means for data collection, wherein a fundamental challenge lies in discovering the “truth” from a multitude of sensing data of varying quality. To address potential privacy leakage issues during the truth discovery process, existing methods often incorporate local differential privacy techniques to protect the data submitted by workers. However, these methods fail to adequately consider the negative impact of Gaussian noise, which reflects worker quality, on the accuracy of the noise “truth”. Moreover, directly applying the Laplace mechanism for privacy protection introduces excessive noise due to the randomness and unbounded nature of the Laplace distribution, resulting in poor precision and utility of truth discovery. Additionally, existing truth discovery methods are either designed for discrete value scenarios or often fail to strictly satisfy Local Differential Privacy (LDP). Therefore, designing a truth discovery algorithm based on mixed distributions that strictly adheres to LDP poses a significant challenge. This is particularly true in continuous value scenarios, where balancing privacy protection with the accuracy of truth discovery, as well as efficiently optimizing the complexity of mixed distribution models to enhance algorithm precision and efficiency, remains a critical issue to be resolved. Methods A novel algorithm, termed Mixture distributiOn-based truth discOvery under local differeNtial privacy (MOON), is proposed. This algorithm primarily considers both the Gaussian noise inherent in the data uploaded by workers, which reflects their quality, and the exogenous Laplace noise injected to protect private data. Based on the mixed noise distribution, new iterative equations for truth discovery are designed. Specifically, each worker first injects Laplace noise into their sensed data and uploads the noise-added data to the server. Subsequently, a probabilistic model combining Gaussian and Laplace noise is constructed and jointly estimated. Finally, the constrained optimization problem is solved using the Lagrange multiplier method to derive iterative equations for worker quality and the “true value” of the noise. Results and Discussions Experimental results demonstrate that, across two real-world datasets, as the privacy budget ε increases, the MOON algorithm exhibits the least impact on utility compared to other benchmark algorithms. Furthermore, when compared to the state-of-the-art TESLA algorithm, MOON achieves at least a 20% improvement in precision (Fig.3). In the context of truth discovery, weight updating is a critical component. Therefore, the experiments also validate the differences between the mixed noise weight distribution derived by the MOON algorithm and the true weight distribution across different datasets (Fig.4). The results indicate that the weight distribution obtained by MOON is closer to the true distribution, aligning with the utility analysis presented in the algorithm analysis section. This is attributed to the smaller scale of noise added to high-quality data. Additionally, the runtime of the MOON algorithm is generally higher than that of the non-privacy-preserving truth discovery algorithm NoPriv, being approximately twice as long (Fig.5), which is consistent with the theoretical analysis. This is due to the injection of Laplace noise into the data uploaded by workers in MOON, necessitating more iterations to converge to the final truth. However, since both runtimes are measured in seconds, this discrepancy is considered acceptable in practical applications. Conclusions Existing truth discovery algorithms that satisfy local differential privacy (LDP) fail to adequately account for the negative impact of Gaussian noise, which reflects worker quality, on the accuracy of the noise "truth." Moreover, while directly applying the Laplace mechanism for noise addition strictly ensures LDP compliance, the randomness and unbounded nature of the Laplace distribution result in excessive noise injection. To address these issues, the MOON algorithm is proposed in this work. Theoretical analysis demonstrates that MOON achieves privacy protection while maintaining low computational and communication complexity. Experimental results on two real-world datasets show that, compared to the latest advancements, MOON improves the precision of the derived "truth" by 20% with minimal additional computational overhead. In future work, the potential social relationships among workers, which may lead to similarities in the data submitted by certain workers, as well as functional dependencies among task attributes, will be leveraged to further enhance the accuracy of truth discovery under local differential privacy.
- Mobile crowd sensing,
- Truth discovery,
- Privacy protection,
- Local Differential Privacy (LDP)

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References(37)

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