  This paper proposes an original approach to cluster multi-component data
sets, including an estimation of the number of clusters. From the construction
of a minimal spanning tree with Prim's algorithm, and the assumption that the
vertices are approximately distributed according to a Poisson distribution, the
number of clusters is estimated by thresholding the Prim's trajectory. The
corresponding cluster centroids are then computed in order to initialize the
generalized Lloyd's algorithm, also known as $K$-means, which allows to
circumvent initialization problems. Some results are derived for evaluating the
false positive rate of our cluster detection algorithm, with the help of
approximations relevant in Euclidean spaces. Metrics used for measuring
similarity between multi-dimensional data points are based on symmetrical
divergences. The use of these informational divergences together with the
proposed method leads to better results, compared to other clustering methods
for the problem of astrophysical data processing. Some applications of this
method in the multi/hyper-spectral imagery domain to a satellite view of Paris
and to an image of the Mars planet are also presented. In order to demonstrate
the usefulness of divergences in our problem, the method with informational
divergence as similarity measure is compared with the same method using
classical metrics. In the astrophysics application, we also compare the method
with the spectral clustering algorithms.
