  Federated learning allows clients to collaboratively train models on datasets
that are acquired in different locations and that cannot be exchanged because
of their size or regulations. Such collected data is increasingly
non-independent and non-identically distributed (non-IID), negatively affecting
training accuracy. Previous works tried to mitigate the effects of non-IID
datasets on training accuracy, focusing mainly on non-IID labels, however
practical datasets often also contain non-IID features. To address both non-IID
labels and features, we propose FedGMCC, a novel framework where a central
server aggregates client models that it can cluster together. FedGMCC
clustering relies on a Monte Carlo procedure that samples the output space of
client models, infers their position in the weight space on a loss manifold and
computes their geometric connection via an affine curve parametrization.
FedGMCC aggregates connected models along their path connectivity to produce a
richer global model, incorporating knowledge of all connected client models.
FedGMCC outperforms FedAvg and FedProx in terms of convergence rates on the
EMNIST62 and a genomic sequence classification datasets (by up to +63%).
FedGMCC yields an improved accuracy (+4%) on the genomic dataset with respect
to CFL, in high non-IID feature space settings and label incongruency.
