Differentially Private $k$-Means Clustering

TL;DR

This paper introduces a hybrid differentially private $k$-means clustering method that combines non-interactive data synopsis publication with interactive refinement, optimizing privacy budget allocation for improved clustering accuracy.

Contribution

It proposes a novel hybrid approach for differentially private $k$-means clustering that balances non-interactive and interactive methods, with analysis and experiments validating its effectiveness.

Findings

Hybrid approach improves clustering accuracy under privacy constraints.

Optimal privacy budget allocation enhances error performance.

Experimental results confirm theoretical analysis.

Abstract

There are two broad approaches for differentially private data analysis. The interactive approach aims at developing customized differentially private algorithms for various data mining tasks. The non-interactive approach aims at developing differentially private algorithms that can output a synopsis of the input dataset, which can then be used to support various data mining tasks. In this paper we study the tradeoff of interactive vs. non-interactive approaches and propose a hybrid approach that combines interactive and non-interactive, using $k$-means clustering as an example. In the hybrid approach to differentially private $k$-means clustering, one first uses a non-interactive mechanism to publish a synopsis of the input dataset, then applies the standard $k$-means clustering algorithm to learn $k$ cluster centroids, and finally uses an interactive approach to further improve these cluster centroids. We analyze the error behavior of both non-interactive and interactive approaches and use such analysis to decide how to allocate privacy budget between the non-interactive step and the interactive step. Results from extensive experiments support our analysis and demonstrate the effectiveness of our approach.