An online algorithm for distributed dictionary learning

This paper proposes a novel algorithm for online distributed dictionary learning, where a set of nodes is requested to collectively estimate a common dictionary via sequentially received data vectors. At each time instance, in which a new datum becomes available, the sparse representation of the data with respect to the estimated dictionary is computed locally at each node by employing a sparsity promoting algorithm. In the sequel, the nodes cooperate in order to collaboratively update the dictionary via the distributed Recursive Least Squares (RLS) algorithm. Numerical examples, both with synthetic and real data, validate that the performance of the proposed algorithm is comparable to that of centralized state of the art algorithms.