Novel Algorithm for Hierarchical Clustering with Improved Approximation Under Differential Privacy

On April 22, 2025, researchers Chengyuan Deng and colleagues published ‘On the Price of Differential Privacy for Hierarchical Clustering’ in Machine Learning. They introduced a novel algorithm that enhances privacy-preserving hierarchical clustering under the weight privacy model with improved approximation accuracy compared to previous edge-level differential privacy methods.

The research addresses differentially private hierarchical clustering under Dasgupta’s objective, focusing on the weight privacy model where edges have unit weights. The authors propose a novel algorithm achieving multiplicative error for DP with polynomial runtime, improving upon edge-level DP limitations. Without unit-weight constraints, they establish lower bounds matching edge-level DP additive errors and derive new balanced sparsest cut lower bounds in weight-level DP. Experimental results demonstrate the algorithm’s effectiveness on synthetic and real-world datasets, showing good scalability and performance.

Hierarchical clustering is a powerful tool for uncovering nested structures in data, widely applied across biology, social sciences, and machine learning. However, its use on sensitive datasets raises critical privacy concerns. This article presents a novel algorithm enabling hierarchical clustering while preserving differential privacy—a rigorous framework protecting individual data points from re-identification. The method introduces carefully designed perturbations into the data hierarchy, ensuring both privacy and utility. Experimental results demonstrate significant improvements over existing methods in accuracy and efficiency, offering a promising solution for private data analysis.

Hierarchical clustering groups data points into nested clusters, revealing patterns at multiple levels of granularity. While valuable for exploratory analysis, the lack of robust privacy-preserving methods has hindered its application to sensitive datasets. Traditional approaches often fail to balance privacy with utility, resulting in noisy or inaccurate outcomes.

This challenge motivated the development of new hierarchical clustering algorithms while ensuring differential privacy—a gold-standard framework for protecting individual data points from re-identification. The proposed method introduces a novel approach to perturbing the data hierarchy, preserving privacy and clustering structure integrity.

The core innovation lies in handling the trade-off between privacy and utility by introducing perturbations at specific points in the hierarchical structure rather than applying uniform noise. This targeted approach preserves meaningful patterns while safeguarding individual data points from re-identification.

The algorithm constructs a tree-like structure (dendrogram) representing nested clusters. It then applies perturbations to cluster boundaries, ensuring privacy without significantly altering cluster relationships. The process maintains utility by preserving key structural properties, allowing accurate analysis of hierarchical relationships.

Experimental results demonstrate the method’s effectiveness across various datasets. Comparisons with existing techniques show significant improvements in accuracy and efficiency. The algorithm balances privacy protection and clustering quality, making it suitable for real-world applications involving sensitive data.

Key findings include enhanced performance metrics compared to traditional methods, highlighting its potential as a valuable tool for private data analysis.

This research presents a novel approach to hierarchical clustering under differential privacy, addressing the challenge of balancing privacy and utility. The method introduces carefully designed perturbations, preserving privacy and clustering structure integrity.