Unsupervised clustering on multi-component datasets: Applications on images and astrophysics data

This paper proposes an original approach to cluster multicomponent data sets with 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. 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 lead to better results than some other clustering methods in the framework of astrophysical data processing. An application of this method in the multi-spectral imagery domain with a satellite view of Paris is also presented.