Some remarks on the DESPOTA algorithm for detecting a partition on a dendrogram

The DESPOTA algorithm was been proposed to automatically detect a partition among those embedded in a dendrogram. The approach exploits a permutation test approach, hence the acronym  DE ndrogram  S licing through a  P ermutati O n Test  A pproach. Unlike the traditional approach used to detect partition, DESPOTA searchs for the final solution in the extended hierarchy consisting in all the possible partitions housed in the dendrogram. In fact, the traditional approach is limited to constant dissimilarity levels (horizontal cut), while DESPOTA can detect also partition whose clusters are characterized by a different dissimilarity level (not horizontal cut). This paper offers both a power study of the method and investigates the use of corrections in order to take into account the multiple testing problem. To this aim, we investigate the use of an adaptive significance level, automatically lowering the value of α thresold when moving down the dendrogram to inspect the clusters. In particular two approaches are compared to adjust p-value, namely the step-up and the stepdown strategy.