<p>Federated clustering is an unsupervised learning method that has emerged in recent years in distributed data environments. Its goal is to discover knowledge from data held by multiple clients. This is achieved by integrating clustering techniques with the federated learning framework, thereby preserving data privacy throughout the process. However, there are significant challenges in data heterogeneity and communication. This paper proposes a new federated learning clustering method, Density Peak and Gaussian distribution Privacy-preserving Federated Clustering (DPG-PFC), to address the data imbalance problem. The core idea of DPG-PFC is as follows: First, clients perform local density peak clustering to extract statistical information of clusters (e.g., variance, mean). Second, the server uses this statistical information to reconstruct a simulated dataset via Gaussian distribution and conducts global re-clustering on the simulated data. To enhance privacy protection, a differential privacy mechanism is adopted to add noise to local data, ensuring privacy security during operations. Experiments on the MNIST dataset validate the effectiveness of DPG-PFC. Specifically, local density clustering resolves inconsistencies in the number of clusters caused by data imbalance. Additionally, the method requires only one communication round, significantly improving communication efficiency.</p>