A study of standardization of variables in cluster analysis

TLDR: The present simulation study examined the standardization problem and found that those approaches which standardize by division by the range of the variable gave consistently superior recovery of the underlying cluster structure.

Abstract: A methodological problem in applied clustering involves the decision of whether or not to standardize the input variables prior to the computation of a Euclidean distance dissimilarity measure. Existing results have been mixed with some studies recommending standardization and others suggesting that it may not be desirable. The existence of numerous approaches to standardization complicates the decision process. The present simulation study examined the standardization problem. A variety of data structures were generated which varied the intercluster spacing and the scales for the variables. The data sets were examined in four different types of error environments. These involved error free data, error perturbed distances, inclusion of outliers, and the addition of random noise dimensions. Recovery of true cluster structure as found by four clustering methods was measured at the correct partition level and at reduced levels of coverage. Results for eight standardization strategies are presented. It was found that those approaches which standardize by division by the range of the variable gave consistently superior recovery of the underlying cluster structure. The result held over different error conditions, separation distances, clustering methods, and coverage levels. The traditionalz-score transformation was found to be less effective in several situations.