Network clustering by graph coloring: An application to astronomical images

In this paper we propose an efficient and polynomial hierarchical clustering technique for unsupervised classification of items being connected by a graph. The output of this algorithm shows the cluster evolution in a divisive way, in such a way that as soon as two items are included in the same cluster they will join a common cluster until the last iteration, in which all the items belong to a singleton cluster. This output can be viewed as a fuzzy clustering in which for each alpha cut we have a standard cluster of the network. The clustering tool we present in this paper allows a hierarchical clustering of related items avoiding some unrealistic constraints that are quite often assumed in clustering problems. The proposed procedure is applied to a hierarchical segmentation problem in astronomical images.