Distributed k-means algorithm

In this paper we provide a fully decentralized and distributed implementation of the k-means clustering algorithm, intended for wireless sensor networks where each node is equipped with sensors and has a limited communication range. The proposed algorithm, by means of one-hop communication, partitions the nodes into groups that have small in-group and large out-group "distances". Depending on the nature of the measurement performed by each node, it is possible to obtain position clustering (i.e., grouping the nodes according to their position), measure clustering (i.e., grouping based on the sensors'measurement such as temperature, speed, etc.) or a hybrid clustering (i.e., considering both the position and the measurement of each node). Since the partitions may not have a relation with the topology of the network--members of the same clusters may not be spatially close--an algorithm for the computation of the clusters'centroid of a sparse and disjoint subset of the nodes is provided. The proposed algorithm converges in finite time, and the result in terms of minimization of the objective function coincides with the centralized k-means algorithm. Some numerical examples illustrate the capabilities of the proposed solution.