Distributed k-means algorithm

TL;DR

This paper introduces a fully distributed k-means clustering algorithm suitable for wireless sensor networks, enabling agents with high-dimensional data to form measure-dependent clusters with minimal communication.

Contribution

It presents a novel distributed implementation of k-means that works without network topology constraints and ensures convergence to the centralized solution.

Findings

Algorithm achieves the same objective function minimization as centralized k-means.

Supports clustering of disconnected sub-clusters within the same group.

Numerical examples demonstrate effective clustering in sensor networks.

Abstract

In this paper we provide a fully distributed implementation of the k-means clustering algorithm, intended for wireless sensor networks where each agent is endowed with a possibly high-dimensional observation (e.g., position, humidity, temperature, etc.) The proposed algorithm, by means of one-hop communication, partitions the agents into measure-dependent groups that have small in-group and large out-group "distances". Since the partitions may not have a relation with the topology of the network--members of the same clusters may not be spatially close--the algorithm is provided with a mechanism to compute the clusters'centroids even when the clusters are disconnected in several sub-clusters.The results of the proposed distributed algorithm coincide, in terms of minimization of the objective function, with the centralized k-means algorithm. Some numerical examples illustrate the capabilities of the proposed solution.