A differential private release method for time series data based on silhouette coefficients

To address the problem that noise perturbation under differential privacy constraints tends to damage clustering structures in time-series clustering result publication, this paper proposes a silhouette coefficient-based anisotropic Gaussian noise generation method. Within the output perturbation framework of clustering results, the silhouette coefficient is utilized to characterize structural differences among clusters, and cluster-level weights are constructed to guide noise allocation. Furthermore, differential privacy noise is formulated as a covariance matrix optimization problem. Under differential privacy constraints, the covariance structure of Gaussian noise is optimized to achieve anisotropic distribution in high-dimensional space, thereby reducing distortion of time-series structural features. In addition, to improve the accuracy of time-series similarity measurement, Dynamic Time Warping (DTW) is adopted as the distance metric, and Principal Component Analysis (PCA) is applied for dimensionality reduction to mitigate the impact of sensitivity on noise magnitude. Experimental results on real-world electricity and water consumption datasets demonstrate that, compared with the privacy-preserving clustering baselines and the conventional isotropic Gaussian mechanism, the proposed method achieves lower differential privacy accuracy loss and mean squared error, while exhibiting better performance in preserving the overall trends and major variation characteristics of time-series data.