Federated FCM: Clustering Under Privacy Requirements

Federated learning addresses the issue of machine learning realized under constraints of privacy and security. While there have been intensive studies on building and analyzing federated regression models, this topic has not been analyzed so far in the area of fuzzy systems. To narrow down this gap, in this study, we formulate and solve a problem of unsupervised federated learning by designing an original federated FCM (F-FCM) clustering which could serve as a basis toward building a spectrum of fuzzy set constructs including rule-based models. Following a general client–server structure, where the local data residing with each client are not available globally and cannot be centralized (as commonly encountered in learning scenarios), the aim is to discover an overall structure across all data. The federated gradient-based optimization realized in the horizontal mode is developed. An overall learning process is derived, which is composed of communicating gradients coming from clients and providing updates of the prototypes at the server side and passing them on to the clients. It is also shown that the relevance of the globally constructed structure is conveniently assessed in terms of granular footprints of the prototypes constructed by the F-FCM. Some illustrative examples are covered to illustrate the efficiency of the developed federated algorithm.