ederated 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 FedGMCC1, 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.@en