  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.
