Privacy-Preserving Vertical K-Means Clustering

2025-04-10

AI Summary

Privacy-preserving K-means clustering over vertically partitioned data remains challenging due to the tension between utility, communication overhead, and rigorous privacy guarantees. Method: This paper proposes the first lightweight collaborative framework integrating homomorphic encryption (HE) and differential privacy (DP) for vertical K-means. It injects DP noise solely into cluster centroids—not raw features—and leverages secure outsourced computation with an optimized Lloyd’s algorithm variant, enabling efficient multi-party clustering without sharing original feature data. Contribution/Results: The framework achieves near-plaintext clustering accuracy while drastically reducing communication cost to 73 MB—99.9% lower than state-of-the-art (SOTA) methods—and completes clustering on 100K samples in just three minutes over a wide-area network. Its core innovation lies in minimizing noise injection and communication complexity to attain an unprecedented utility–privacy trade-off.

Technology Category

• Machine Learning: Clustering
• Data Mining & Knowledge Management: Data Compression
• Search and Optimization: Distributed Search

Application Category

• Security and Privacy: Privacy-enhancing technologies
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

Clustering is a fundamental data processing task used for grouping records based on one or more features. In the vertically partitioned setting, data is distributed among entities, with each holding only a subset of those features. A key challenge in this scenario is that computing distances between records requires access to all distributed features, which may be privacy-sensitive and cannot be directly shared with other parties. The goal is to compute the joint clusters while preserving the privacy of each entity's dataset. Existing solutions using secret sharing or garbled circuits implement privacy-preserving variants of Lloyd's algorithm but incur high communication costs, scaling as O(nkt), where n is the number of data points, k the number of clusters, and t the number of rounds. These methods become impractical for large datasets or several parties, limiting their use to LAN settings only. On the other hand, a different line of solutions rely on differential privacy (DP) to outsource the local features of the parties to a central server. However, they often significantly degrade the utility of the clustering outcome due to excessive noise. In this work, we propose a novel solution based on homomorphic encryption and DP, reducing communication complexity to O(n+kt). In our method, parties securely outsource their features once, allowing a computing party to perform clustering operations under encryption. DP is applied only to the clusters' centroids, ensuring privacy with minimal impact on utility. Our solution clusters 100,000 two-dimensional points into five clusters using only 73MB of communication, compared to 101GB for existing works, and completes in just under 3 minutes on a 100Mbps network, whereas existing works take over 1 day. This makes our solution practical even for WAN deployments, all while maintaining accuracy comparable to plaintext k-means algorithms.

Problem

• Privacy-preserving clustering for vertically partitioned data.
• Reducing high communication costs in existing secure methods.
• Balancing privacy and utility in distributed feature clustering.

Innovation

• Uses homomorphic encryption for secure outsourcing
• Applies differential privacy to centroids only
• Reduces communication cost to O(n+kt)