Centrality and Distribution of Partitions according to the Transfer Distance

The comparison of partitions is a central topic in clustering, as well for comparing partitioning algorithms as for classifying nominal variables. In this paper, we deal with the transfer distance between partitions, defined as the minimum number of transfers of one element from its class to another (eventually empty) necessary to turn one partition into the other one. We study the distribution of partitions according to their transfer distances to some reference partitions. Then we design criteria to define when two partitions can be considered as far or as close. Last, we look for the features of the partitions which can be considered as central, i.e. partitions such that the other partitions are relatively close to them.