Application of the covariance matrix clustering algorithm for partitioning joint sets having various joint pole sizes and densities

Abstract

An analysis of data collected on rock discontinuities mostly requires the data to be separated into sets. An automatic clustering algorithm that assists in identification of joint sets is always desired. Several algorithms have been proposed, most of which are based on the widely used fuzzy K-means method in which the optimization step involves minimizing the sum of squared distances between objects and the centroids of clusters. Empirical studies have demonstrated that this method tends to generate equally sized clusters, which means clusters of different sizes cannot be adequately distinguished (equal-size problem). This paper introduces the application of a clustering method that applies an optimization criterion based on the estimated covariance matrix to overcome the aforementioned equal-size problem of the K-means clustering scheme. The applicability of the method is demonstrated using both artificial and field data with low dimensionality.