Federated Soft Clustering via Generalized Total Variation Minimization

The paper introduces federated soft clustering for devices in a federated learning network, each fitting a personalized Gaussian mixture model. It proposes Generalized Total Variation Minimization (GTVMin) to couple local maximum likelihood problems via a graph regularizer that penalizes discrepancies between connected nodes’ models. Three discrepancy measures are compared: a squared Euclidean distance requiring component matching, a Monte‑Carlo approximated Kullback‑Leibler divergence, and a closed‑form maximum mean discrepancy; all are optimized with synchronous projected gradient updates, with a convergence guarantee for the smooth MMD instance.

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