  A key challenge in federated learning applications is the statistical
heterogeneity of local datasets. Clustered federated learning addresses this
challenge by identifying clusters of local datasets that are approximately
homogeneous. One recent approach to clustered federated learning is generalized
total variation minimization (GTVMin). This approach requires a similarity
graph which can be obtained by domain expertise or in a data-driven fashion via
graph learning techniques. Under a widely applicable clustering assumption, we
derive an upper bound the deviation between GTVMin solutions and their
cluster-wise averages. This bound provides valuable insights into the
effectiveness and robustness of GTVMin in addressing statistical heterogeneity
within federated learning environments.
