Distributed k-winners-take-all via multiple neural networks with inertia

This paper is dedicated to solving the k-winners-take-all problem with large-scale input signals in a distributed manner. According to the decomposition of global input signals, a novel dynamical system consisting of multiple coordinated neural networks is proposed for finding the k largest inputs. In the system, each neural network is designed to tackle its available partial inputs only for a local objective k_i (k_i≤k). Simultaneously, a consensus-based approach is adopted to coordinate multiple neural networks for achieving the global objective k. In addition, an inertial term is introduced in each neural network for regulating its transient behavior, which has the potential of accelerating the convergence. By developing a cocoercive operator, we theoretically prove that the multiple neural networks with inertial terms converge asymptotically/exponentially to the k-winners-take-all solution exactly from arbitrary initial states for whatever decomposition of inputs and objective. Furthermore, some extensions to distributed constrained k-winners-take-all are also investigated. Finally, simulation results are presented to substantiate the effectiveness of the proposed system as well as its superior performance over existing distributed networks.