Fuzzy C-Means Clustering Algorithm Based on Mixed Noise-aware under Local Differential Privacy

ZHANG Pengfei; CHENG Jun; ZHANG Zhikun; FANG Xianjin; SUN Li; WANG Jie; JIANG Rong

doi:10.11999/JEIT241067

Volume 47 Issue 3

Mar. 2025

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ZHANG Pengfei, CHENG Jun, ZHANG Zhikun, FANG Xianjin, SUN Li, WANG Jie, JIANG Rong. Fuzzy C-Means Clustering Algorithm Based on Mixed Noise-aware under Local Differential Privacy[J]. Journal of Electronics & Information Technology, 2025, 47(3): 739-757. doi: 10.11999/JEIT241067

Citation:

ZHANG Pengfei, CHENG Jun, ZHANG Zhikun, FANG Xianjin, SUN Li, WANG Jie, JIANG Rong. Fuzzy C-Means Clustering Algorithm Based on Mixed Noise-aware under Local Differential Privacy[J]. Journal of Electronics & Information Technology, 2025, 47(3): 739-757. doi: 10.11999/JEIT241067

Citation:

ZHANG Pengfei, CHENG Jun, ZHANG Zhikun, FANG Xianjin, SUN Li, WANG Jie, JIANG Rong. Fuzzy C-Means Clustering Algorithm Based on Mixed Noise-aware under Local Differential Privacy[J]. Journal of Electronics & Information Technology, 2025, 47(3): 739-757. doi: 10.11999/JEIT241067

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Fuzzy C-Means Clustering Algorithm Based on Mixed Noise-aware under Local Differential Privacy

doi: 10.11999/JEIT241067 cstr: 32379.14.JEIT241067

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.
College of Computer Science and Technology, Zhejiang University, Hangzhou 310058, China
4.
School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China
5.
School of Safety Science and Engineering, Anhui University of Science and Technology, Huainan 232001, China

Funds: The Scientific Research 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: 2024-12-04
Rev Recd Date: 2025-02-25

Available Online: 2025-03-07

Publish Date: 2025-03-01

Abstract

Abstract

Objective In big data and Internet of Things (IoT) applications, clustering analysis of collected data is crucial for enhancing user experience. To mitigate privacy risks from using raw data directly, Local Differential Privacy (LDP) techniques are often employed. However, existing LDP clustering studies either require interactive execution, consuming significant privacy budgets, or fail to balance Gaussian noise in clustering data with Laplacian noise for LDP protection, resulting in low clustering accuracy. Moreover, distance metrics for similarity measurement are chosen arbitrarily without fully utilizing the noise characteristics of user-submitted noisy data. This study designs a hybrid noise-aware distance calculation method integrated into the fuzzy C-means clustering algorithm, effectively reducing noise impact on clustering results while protecting data privacy, ensuring both privacy security and clustering quality. It provides a robust solution for sensitive information processing in high-dimensional data environments. Methods This paper innovatively proposes a mixed noise-aware Fuzzy C-Means clustering algorithm (mnFCM) under LDP. The core idea is to model both Gaussian noise (representing data quality) and Laplacian noise (for data protection) in uploaded user data by constructing a more accurate mixed distribution model, and design a mixed noise-aware distance to replace Euclidean distance for measuring similarity between samples and cluster centers. Specifically, in mnFCM, this paper first designs a mixed noise-aware distance calculation method. On this basis, a new objective function for the algorithm is proposed, and a solution method is designed based on the Lagrange multiplier method. Finally, the convergence of the solution algorithm is theoretically analyzed. Results and Discussions The experimental results show that as the privacy budget ε increases, the performance of various clustering algorithms generally improves. Notably, mnFCM achieves at least a 8.5% improvement in accuracy compared to the state-of-the-art PrivPro algorithm (Fig.1). This is because mnFCM innovatively considers both Gaussian noise (reflecting data quality) and Laplacian noise (for LDP protection), designing a hybrid noise-aware distance metric to enhance sample similarity measurement, thereby effectively protecting privacy while balancing clustering performance. Experiments on the fuzziness parameter m reveal that when m=2, all algorithms reach peak F-Measure values and lowest Entropy values (Fig.2), strongly validating m=2 as the optimal balance point for clustering effectiveness. Additionally, running time of mnFCM is 1.0 to 1.4 times that of the non-privacy-preserving Nopriv algorithm (Table 2), due to its refined noise processing mechanism. Ablation experiments demonstrate that the MixDis scheme achieves the best clustering performance on both NG and UW datasets (Fig.4), as it considers both Laplacian and Gaussian noise, making the clustered data more robust. Comparative analysis on the synthetic dataset Syn with other privacy-preserving clustering algorithms shows that DP-DPCL+ consistently outperforms DP-DPCL, and DPC+ consistently outperforms DPC (Fig.5). In addition, by varying the values of the four adjustable parameters—privacy budget ε, sample size N, dimension K, and cluster number C—it is evident that the mnFCM method outperforms other privacy protection schemes (Fig. 6). Conclusions This paper addresses the privacy protection issue in fuzzy clustering algorithms by simultaneously considering Gaussian noise (reflecting data quality) and Laplacian noise (for LDP protection), and innovatively proposes a mixed noise-aware fuzzy C-means clustering algorithm, mnFCM, satisfying LDP to balance privacy security and clustering quality. It designs a mixed noise-aware distance calculation method, formulates a new objective function, and solves it using the Lagrange multiplier method, while theoretically analyzing the algorithm’s convergence. Theoretical analysis shows that the algorithm strictly satisfies LDP, is closer to non-private cluster centroids compared to baseline algorithms, and has similar complexity to non-private algorithms. Experiments demonstrate that the algorithm improves clustering accuracy by 10%～15% on real datasets compared to baseline privacy-preserving algorithms. However, a limitation of this study is that the privacy budget calculation for Laplacian noise in the mixed noise setting may be influenced by Gaussian noise. In future research, the adaptive noise proportion allocation strategies, such as dynamically adjusting the weights of Gaussian/Laplacian noise, will be further explored to optimize the privacy-utility trade-off.
- Clustering analysis,
- Privacy protection,
- Local Differential Privacy (LDP),
- Fuzzy C-Means (FCM) clustering,
- Laplace mechanism

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References(36)

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