  This paper considers a network of sensors without fusion center that may be
difficult to set up in applications involving sensors embedded on autonomous
drones or robots. In this context, this paper considers that the sensors must
perform a given clustering task in a fully decentralized setup. Standard
clustering algorithms usually need to know the number of clusters and are very
sensitive to initialization, which makes them difficult to use in a fully
decentralized setup. In this respect, this paper proposes a decentralized
model-based clustering algorithm that overcomes these issues. The proposed
algorithm is based on a novel theoretical framework that relies on hypothesis
testing and robust M-estimation. More particularly, the problem of deciding
whether two data belong to the same cluster can be optimally solved via Wald's
hypothesis test on the mean of a Gaussian random vector. The p-value of this
test makes it possible to define a new type of score function, particularly
suitable for devising an M-estimation of the centroids. The resulting
decentralized algorithm efficiently performs clustering without prior knowledge
of the number of clusters. It also turns out to be less sensitive to
initialization than the already existing clustering algorithms, which makes it
appropriate for use in a network of sensors without fusion center.
