Standardization and Weighting of Variables for the Fuzzy K-Means Clustering of Discontinuity Data

ABSTRACT: In the analysis of discontinuity data, it is often not known initially which variables are most useful in distinguishing between the different fracture groupings or sets. Cluster analysis tools are particularly vulnerable to the presence of variables that are essentially noise variables, because such variables can mask the true cluster structure of the data leading to poor cluster recovery. It is therefore essential to reduce the influence of unimportant variables by assigning importance weights to all variables involved in a cluster analysis. One other associated problem in cluster analysis is that the different measurement scales of different variables can cause some variables to dominate a cluster analysis solely because of the magnitudes of their readings and not because of importance. Variable standardization is the technique commonly used to solve this problem. This paper looks at the issues surrounding variable weighting and standardization, and proposes algorithms for addressing the difficulties associated with it in fuzzy K-means cluster analysis.