Simplicial clustering using the $\alpha$--transformation

We introduce two simplicial clustering approaches for compositional data, that are adaptations of the $K$--means and of the Gaussian mixture models algorithms, by employing the $\alpha$--transformation. By utilizing clustering validation indices we can decide on the number of clusters and choose the value of $\alpha$ for the $K$--means, while for the model-based clustering approach information criteria complete this task. Extensive simulation studies compare the performance of these two approaches and a real dataset illustrates their performance in real world settings.