Distributed Finite-Time k-means Clustering with Quantized Communucation and Transmission Stopping

In this paper, we present a distributed version of the k-means algorithm for multi-agent systems with directed communication links. The goal of k-means is to partition the network’s agents in mutually exclusive sets (groups) such that agents in the same set have (and possibly share) similar information and are able to calculate a representative value for their group. Our distributed algorithm allows each node to transmit quantized values in an event-driven fashion, and exhibits distributed stopping capabilities. Transmitting quantized values leads to more efficient usage of the available bandwidth and reduces the communication bottleneck, whereas distributed stopping preserves available resources. We characterize the properties of the proposed distributed algorithm and show that its execution (on any static and strongly connected digraph) will partition all agents in mutually exclusive clusters in finite time. We conclude with examples that illustrate the operation, performance, and potential advantages of the proposed algorithm.