  Federated clustering, an integral aspect of federated machine learning,
enables multiple data sources to collaboratively cluster their data,
maintaining decentralization and preserving privacy. In this paper, we
introduce a novel federated clustering algorithm named Dynamically Weighted
Federated k-means (DWF k-means) based on Lloyd's method for k-means clustering,
to address the challenges associated with distributed data sources and
heterogeneous data. Our proposed algorithm combines the benefits of traditional
clustering techniques with the privacy and scalability benefits offered by
federated learning. The algorithm facilitates collaborative clustering among
multiple data owners, allowing them to cluster their local data collectively
while exchanging minimal information with the central coordinator. The
algorithm optimizes the clustering process by adaptively aggregating cluster
assignments and centroids from each data source, thereby learning a global
clustering solution that reflects the collective knowledge of the entire
federated network. We address the issue of empty clusters, which commonly
arises in the context of federated clustering. We conduct experiments on
multiple datasets and data distribution settings to evaluate the performance of
our algorithm in terms of clustering score, accuracy, and v-measure. The
results demonstrate that our approach can match the performance of the
centralized classical k-means baseline, and outperform existing federated
clustering methods like k-FED in realistic scenarios.
