One-Shot Federated Clustering Based on Stable Distance Relationships

Federated clustering (FC) is an emerging and important topic in data clustering research. However, for existing works, there are two challenging issues as follows. 1) FC does not perform well on non-IID data. 2) Differential privacy is a common-used way to protect raw data in FC, but there is no solid theoretical basis for selecting privacy budget <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\epsilon$</tex-math></inline-formula> in Laplacian noise, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\epsilon$</tex-math></inline-formula> is randomly set in most algorithms. In this article, we propose a new framework called NN-FC for addressing the above-mentioned issues. Specifically, 1) we provide a rigorous mathematical proof when selecting <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\epsilon$</tex-math></inline-formula>, we have shown that when the value of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\epsilon$</tex-math></inline-formula> satisfies certain conditions, the neighbor relationship of data points before and after adding Laplacian noises remains unchanged. 2) According to 1), we propose a new method of obtaining global cluster centers based on distance relationships at the server, and the results of clustering the original data and clustering the privacy data become close. The experimental results show that NN-FC performs better than eight traditional and state-of-the-art (SOTA) centralized (nonfederated) clustering algorithms. In particular, NN-FC performs better than two SOTA FC frameworks k-FED (ICML2021) and MUFC (ICLR2023).