On distance measures for the fuzzy K-means algorithm for joint data

The analysis of data collected on rock discontinuities often requires that the data be separated into joint sets or groups. A statistical tool that facilitates the automatic identification of groups of clusters of observations in a data set is cluster analysis. The fuzzy K-means cluster technique has been successfully applied to the analysis of joint survey data. As is the case with all clustering algorithms, the results of an analysis performed with the fuzzy K-means algorithm for discontinuity data are highly dependent on the distance metric employed in the analysis. This paper explores the significant issues surrounding the choice and use of various distance measures for clustering joint survey data. It also proposes an analogue of the Mahalanobis distance norm (used for data in Euclidean space) for clustering spherical data. Sample applications showing the greater flexibility and power of the new distance measure over the originally proposed distance metric for spherical data are given in the paper.