Subspace Parsimonious Dictionary Learning and its use in Federated Learning

A federated dictionary learning problem, in which the edge devices have data with different statistical properties, is considered. A dictionary learning cost function that can lead to dictionaries that do not exhaust their full representation capabilities is proposed. The edge devices utilize this algorithm to design the local dictionaries. Likewise, a new aggregation rule is proposed for the central server, that takes into account the particular form of the local dictionaries. Simulation results were conducted that demonstrated that the proposed approach leads to solutions that achieve smaller root mean square error, are more sparse, but most importantly, require significantly smaller numbers of federated learning rounds to achieve some required error.