Consensus-based partitions in the space of ordered partitions

摘要

The paper presents a method of determining a representation of ordered partitions,i.e. a partition to which the sum of distance from fixed partitions is minimal. Two metrics are proposed as measures of distance between ordered partitions. The first metric is equal to the minimum number of element moves necessary to transform a partition into another one, and the second one equals the sum of weights of these element moves. Criteria of selecting best reprsentations of chosen ordered partitions are also presented.