Distributed tensor completion over networks

The aim of this paper is to propose a novel distributed strategy for tensor completion, where (partial) data are collected over a network of agents with sparse, but connected, topology. The method hinges on the canonical polyadic decomposition, also known as PARAFAC, to complete the low-rank tensor in a distributed fashion. To deal with the nonconvex and distributed nature of the learning problem, we exploit a convexification/decomposition technique based on successive convex approximations, while using dynamic consensus to diffuse information over the network and force asymptotic agreement among the agents. Asymptotic convergence to stationary solutions of the centralized problem is established under mild conditions. Finally, numerical results assess the performance of the proposed method over both synthetic and real data.