  With the increasing importance of data privacy protection, various
privacy-preserving machine learning methods have been proposed. In the
clustering domain, various algorithms with a federated learning framework
(i.e., federated clustering) have been actively studied and showed high
clustering performance while preserving data privacy. However, most of the base
clusterers (i.e., clustering algorithms) used in existing federated clustering
algorithms need to specify the number of clusters in advance. These algorithms,
therefore, are unable to deal with data whose distributions are unknown or
continually changing. To tackle this problem, this paper proposes a
privacy-preserving continual federated clustering algorithm. In the proposed
algorithm, an adaptive resonance theory-based clustering algorithm capable of
continual learning is used as a base clusterer. Therefore, the proposed
algorithm inherits the ability of continual learning. Experimental results with
synthetic and real-world datasets show that the proposed algorithm has superior
clustering performance to state-of-the-art federated clustering algorithms
while realizing data privacy protection and continual learning ability. The
source code is available at \url{https://github.com/Masuyama-lab/FCAC}.
