  Supervised federated learning (FL) enables multiple clients to share the
trained model without sharing their labeled data. However, potential clients
might even be reluctant to label their own data, which could limit the
applicability of FL in practice. In this paper, we show the possibility of
unsupervised FL whose model is still a classifier for predicting class labels,
if the class-prior probabilities are shifted while the class-conditional
distributions are shared among the unlabeled data owned by the clients. We
propose federation of unsupervised learning (FedUL), where the unlabeled data
are transformed into surrogate labeled data for each of the clients, a modified
model is trained by supervised FL, and the wanted model is recovered from the
modified model. FedUL is a very general solution to unsupervised FL: it is
compatible with many supervised FL methods, and the recovery of the wanted
model can be theoretically guaranteed as if the data have been labeled.
Experiments on benchmark and real-world datasets demonstrate the effectiveness
of FedUL. Code is available at https://github.com/lunanbit/FedUL.
