Comparative analysis of the optimum cluster number determination algorithms in clustering GPS velocities

Abstract

The Global Positioning System (GPS), although it has existed for only 30 years, is an important source for active tectonics, resulting in estimates of plate motions very close to geologic estimates over millions of years. GPS is also used for elastic block models to calculate slip rates for a better understanding of Earth's active crustal deformation. GPS-derived velocity fields may be used as the basis for clustering analysis to create a preliminary definition of block geometry. In this study, we used published horizontal velocity fields to evaluate the effects of data dependences on determining the optimum number of clusters with algorithms. For this purpose, we used different variations of velocity fields in Turkey and tested four different algorithms that are Davies-Bouldin index, the elbow method, GAP statistics algorithm and the silhouette method. We also clustered velocity components with the k-means technique and compared the results with previous studies.