Simplicial clustering using the $α$--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 $α$--transformation. By utilizing clustering validation indices we can decide on the number of clusters and choose the value of $α$ 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 data set illustrates their performance in real world settings.