A fast partitioning algorithm using adaptive Mahalanobis clustering with application to seismic zoning

In this paper we construct an efficient adaptive Mahalanobis k-means algorithm. In addition, we propose a new efficient algorithm to search for a globally optimal partition obtained by using the adoptive Mahalanobis distance-like function. The algorithm is a generalization of the previously proposed incremental algorithm (Scitovski and Scitovski, 2013). It successively finds optimal partitions with k=2,3,… clusters. Therefore, it can also be used for the estimation of the most appropriate number of clusters in a partition by using various validity indexes. The algorithm has been applied to the seismic catalogues of Croatia and the Iberian Peninsula. Both regions are characterized by a moderate seismic activity. One of the main advantages of the algorithm is its ability to discover not only circular but also elliptical shapes, whose geometry fits the faults better. Three seismogenic zonings are proposed for Croatia and two for the Iberian Peninsula and adjacent areas, according to the clusters discovered by the algorithm.