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Recent demands on data privacy have called for federated learning (FL) as anew distributed learning paradigm in massive and heterogeneous networks.Although many FL algorithms have been proposed, few of them have considered thematrix factorization (MF) model, which is known to have a vast number of signalprocessing and machine learning applications. Different from the existing FLalgorithms that are designed for smooth problems with single block ofvariables, in federated MF (FedMF), one has to deal with challenging non-convexand non-smooth problems (due to constraints or regularization) with two blocksof variables. In this paper, we address the challenge by proposing two newFedMF algorithms, namely, FedMAvg and FedMGS, based on the model averaging andgradient sharing principles, respectively. Both FedMAvg and FedMGS adoptmultiple steps of local updates per communication round to speed upconvergence, and allow only a randomly sampled subset of clients to communicatewith the server for reducing the communication cost. Convergence analyses forthe two algorithms are respectively presented, which delineate the impacts ofdata distribution, local update number, and partial client communication on thealgorithm performance. By focusing on a data clustering task, extensiveexperiment results are presented to examine the practical performance of bothalgorithms, as well as demonstrating their efficacy over the existingdistributed clustering algorithms.

Federated Matrix Factorization: Algorithm Design and Application to Data Clustering