Utility-efficient Differentially Private K-means Clustering based on Cluster Merging

TL;DR

This paper introduces DP-KCCM, a differentially private k-means clustering algorithm that enhances utility through adaptive noise addition and cluster merging, with theoretical privacy guarantees and improved experimental results.

Contribution

The paper presents a novel DP-kmeans algorithm combining adaptive noise and cluster merging, significantly improving clustering utility under differential privacy.

Findings

Cluster merging with equal noise improves utility.

Adaptive noise alone does not improve utility.

Combining adaptive noise and cluster merging significantly enhances utility.

Abstract

Differential privacy is widely used in data analysis. State-of-the-art $k$-means clustering algorithms with differential privacy typically add an equal amount of noise to centroids for each iterative computation. In this paper, we propose a novel differentially private $k$-means clustering algorithm, DP-KCCM, that significantly improves the utility of clustering by adding adaptive noise and merging clusters. Specifically, to obtain $k$ clusters with differential privacy, the algorithm first generates $n \times k$ initial centroids, adds adaptive noise for each iteration to get $n \times k$ clusters, and finally merges these clusters into $k$ ones. We theoretically prove the differential privacy of the proposed algorithm. Surprisingly, extensive experimental results show that: 1) cluster merging with equal amounts of noise improves the utility somewhat; 2) although adding adaptive noise only does not improve the utility, combining both cluster merging and adaptive noise further improves the utility significantly.