One-Shot Secure Federated <i>K</i>-Means Clustering Based on Density Cores

Federated clustering (FC) performs well in independent and identically distributed (IID) scenarios, but it does not perform well in non-IID scenarios. In addition, existing methods lack proof of strict privacy protection. To address the above issues, we propose a new secure federated k-means clustering framework to achieve better clustering results under privacy requirements. Specifically, for the clients, we use cluster centers (representative points) generated by k-means to represent the corresponding clusters. These representative points can effectively preserve the structure of the local data and they are encrypted by differential privacy. For the server, we propose two methods to reprocess the uploaded encrypted representative points to obtain better final cluster centers, one uses k-means, and the other considers the improved density peaks (density cores) as final centers and then sends them back to the clients. Finally, each client assigns local data to their nearest centers. Experimental results show that the proposed methods perform better than several centralized (nonfederated) classical clustering algorithms [k-means, density-based spatial clustering of applications with noise (DBSCAN), and density peak clustering (DPC)] and state-of-the-art (SOTA) centralized clustering algorithms in most cases. In particular, the proposed algorithms perform better than the SOTA FC framework k-FED (ICML2021) and MUFC (ICLR2023).