A New Clustering Approach for Partitioning Directional Data

A new clustering approach is developed for partioning of directional data, which is based on vector quantization. Directional data are grouped into a certain number of disjoint isotropic clusters and - at the same time - the average dip direction and the average dip angle are calculated for each group. The method is based on a new and mathematically self-consistent approach. Grouping is achieved by minimizing the average distance between the data points and the average values which characterize the cluster to which the data points belong. The distance between directional data is measured by the arc-length between the corresponding poles on the unit sphere. The algorithm is fast and shows good clustering results compared to the counting method of Shanley and Mahtab and the expert-supervised grouping method developed by Pecher. No heuristics is being used, because the grouping of data points, the binary assignment of new data points to clusters, and the calculation of the average cluster values are based on the same cost function. The new method minimizes manual interactions and does not require the calculation of a contour density plot. In ongoing research investigations, the new approach will be extended to probabilistic assignments (soft-clustering), and to grouping problems which involve anisotropic clusters.

The clustering algorithm (Klose et al. 2005) is below. Pls. except the plug-in and you can use the software to cluster orientation data (pole or plane coordinates), such as pole_data_example.dat. Clustering parameters are given a priori. To reach an optimal clustering result you may need to change these parameters. Software documentation you can find under Documentation.