Skewed Distributions or Transformations? Modelling Skewness for a Cluster Analysis

Because of its mathematical tractability, the Gaussian mixture model holds a special place in the literature for clustering and classification. For all its benefits, however, the Gaussian mixture model poses problems when the data is skewed or contains outliers. Because of this, methods have been developed over the years for handling skewed data, and fall into two general categories. The first is to consider a mixture of more flexible skewed distributions, and the second is based on incorporating a transformation to near normality. Although these methods have been compared in their respective papers, there has yet to be a detailed comparison to determine when one method might be more suitable than the other. Herein, we provide a detailed comparison on many benchmarking datasets, as well as describe a novel method to assess cluster separation.