  This paper deals with the problem of statistical and system heterogeneity in
a cross-silo Federated Learning (FL) framework where there exist a limited
number of Consumer Internet of Things (CIoT) devices in a smart building. We
propose a novel Graph Signal Processing (GSP)-inspired aggregation rule based
on graph filtering dubbed ``G-Fedfilt''. The proposed aggregator enables a
structured flow of information based on the graph's topology. This behavior
allows capturing the interconnection of CIoT devices and training
domain-specific models. The embedded graph filter is equipped with a tunable
parameter which enables a continuous trade-off between domain-agnostic and
domain-specific FL. In the case of domain-agnostic, it forces G-Fedfilt to act
similar to the conventional Federated Averaging (FedAvg) aggregation rule. The
proposed G-Fedfilt also enables an intrinsic smooth clustering based on the
graph connectivity without explicitly specified which further boosts the
personalization of the models in the framework. In addition, the proposed
scheme enjoys a communication-efficient time-scheduling to alleviate the system
heterogeneity. This is accomplished by adaptively adjusting the amount of
training data samples and sparsity of the models' gradients to reduce
communication desynchronization and latency. Simulation results show that the
proposed G-Fedfilt achieves up to $3.99\% $ better classification accuracy than
the conventional FedAvg when concerning model personalization on the
statistically heterogeneous local datasets, while it is capable of yielding up
to $2.41\%$ higher accuracy than FedAvg in the case of testing the
generalization of the models.
