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

TL;DR

This paper introduces a distributed $k$-means clustering algorithm for multi-agent systems that uses quantized communication and distributed stopping, ensuring finite-time convergence and efficient resource usage.

Contribution

It presents a novel distributed $k$-means algorithm with quantized communication and stopping capabilities, applicable to directed graphs, with proven finite-time convergence.

Findings

Algorithm guarantees finite-time clustering

Quantized communication reduces bandwidth usage

Distributed stopping saves computational resources

Abstract

In this paper, we present a distributed algorithm which implements the $k$-means algorithm in a distributed fashion 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.During the operation of our distributed algorithm, each node (i) transmits quantized values in an event-driven fashion, and (ii) exhibits distributed stopping capabilities. Transmitting quantized values leads to more efficient usage of the available bandwidth and reduces the communication bottleneck. Also, in order to preserve available resources, nodes are able to distributively determine whether they can terminate the operation of the proposed algorithm. 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 to mutually exclusive clusters in finite time. We conclude with examples that illustrate the operation, performance, and potential advantages of the proposed algorithm.