Locally Differentially Private Graph Clustering via the Power Iteration Method

TL;DR

This paper introduces a new locally differentially private graph clustering algorithm based on the power iteration method, which achieves accurate results with a constant privacy budget on well-clustered graphs with high minimum degree.

Contribution

The paper presents an interactive power iteration-based algorithm for local differential privacy in graph clustering, overcoming limitations of previous spectral methods that required larger privacy budgets.

Findings

Outperforms randomized response spectral clustering on real graphs

Achieves accurate clustering with constant privacy budget on well-clustered graphs

Works on graphs with minimum degree  ilde{\u2207} ext{O}(\

Abstract

We propose a locally differentially private graph clustering algorithm. Previous works have explored this problem, including approaches that apply spectral clustering to graphs generated via the randomized response algorithm. However, these methods only achieve accurate results when the privacy budget is in $\Omega(\log n)$, which is unsuitable for many practical applications. In response, we present an interactive algorithm based on the power iteration method. Given that the noise introduced by the largest eigenvector constant can be significant, we incorporate a technique to eliminate this constant. As a result, our algorithm attains local differential privacy with a constant privacy budget when the graph is well-clustered and has a minimum degree of $\tilde{\Omega}(\sqrt{n})$. In contrast, while randomized response has been shown to produce accurate results under the same minimum degree condition, it is limited to graphs generated from the stochastic block model. We perform experiments to demonstrate that our method outperforms spectral clustering applied to randomized response results.