A Distributed k-Winners-Take-All Model With Binary Consensus Protocols

This article concentrates on solving the k-winner-stake-all (kWTA) problem with large-scale inputs in a distributed setting. We propose a multiagent system with a relatively simple structure, in which each agent is equipped with a 1-D system and interacts with others via binary consensus protocols. That is, only the signs of the relative state information between neighbors are required. By virtue of differential inclusion theory, we prove that the system converges from arbitrary initial states. In addition, we derive the convergence rate as O(1/t). Furthermore, in comparison to the existing models, we introduce a novel comparison filter to eliminate the resolution ratio requirement on the input signal, that is, the difference between the kth and (k + 1)th largest inputs must be larger than a positive threshold. As a result, the proposed distributed kWTA model is capable of solving the kWTA problem, even when more than two elements of the input signal share the same value. Finally, we validate the effectiveness of the theoretical results through two simulation examples.

Automated summary

This article presents a solution to the k-winner-take-all (kWTA) problem with large-scale inputs in a distributed setting. A multiagent system is proposed, where each agent has a 1-D system and interacts with others through binary consensus protocols. The system convergence is proven using differential inclusion theory, and a novel comparison filter is introduced to eliminate the resolution ratio requirement on the input signal.