# Private Hierarchical Clustering and Efficient Approximation

## TL;DR

This paper presents a privacy-preserving protocol for hierarchical clustering that balances utility and privacy, with scalable approximations and real-world performance demonstrating its effectiveness on large datasets.

## Contribution

It introduces a formal security framework and a two-party protocol for privacy-preserving hierarchical clustering, including optimized and scalable approximation methods.

## Key findings

- Secure protocol achieves 97.09% accuracy on large datasets.
- End-to-end execution takes 35 seconds for over 1 million samples.
- Scalable variants maintain high utility with improved efficiency.

## Abstract

In collaborative learning, multiple parties contribute their datasets to jointly deduce global machine learning models for numerous predictive tasks. Despite its efficacy, this learning paradigm fails to encompass critical application domains that involve highly sensitive data, such as healthcare and security analytics, where privacy risks limit entities to individually train models using only their own datasets. In this work, we target privacy-preserving collaborative hierarchical clustering. We introduce a formal security definition that aims to achieve the balance between utility and privacy and present a two-party protocol that provably satisfies it. We then extend our protocol with: (i) an optimized version for the single-linkage clustering, and (ii) scalable approximation variants. We implement all our schemes and experimentally evaluate their performance and accuracy on synthetic and real datasets, obtaining very encouraging results. For example, end-to-end execution of our secure approximate protocol for over 1M 10-dimensional data samples requires 35sec of computation and achieves 97.09% accuracy.