Towards Federated Clustering: A Federated Fuzzy $c$-Means Algorithm (FFCM)

Federated Learning (FL) is a setting where multiple parties with distributed data collaborate in training a joint Machine Learning (ML) model while keeping all data local at the parties. Federated clustering is an area of research within FL that is concerned with grouping together data that is globally similar while keeping all data local. We describe how this area of research can be of interest in itself, or how it helps addressing issues like non-independently-identically-distributed (i.i.d.) data in supervised FL frameworks. The focus of this work, however, is an extension of the federated fuzzy $c$-means algorithm to the FL setting (FFCM) as a contribution towards federated clustering. We propose two methods to calculate global cluster centers and evaluate their behaviour through challenging numerical experiments. We observe that one of the methods is able to identify good global clusters even in challenging scenarios, but also acknowledge that many challenges remain open.