Core Potentials: The Consensus Segmentation Conjecture

Segmentations are partitions of an ordered set into non-overlapping intervals. The Consensus Segmentation or Segmentation Aggregation problem is a special case of the median problems with applications in time series analysis and computational biology. A wide range of dissimilarity measures for segmentations can be expressed in terms of potentials, a special type of set-functions. In this contribution, we shed more light on the properties of potentials, and how such properties affect the solutions of the Consensus Segmentation problem. In particular, we disprove a conjecture stated in 2021, and we provide further insights into the theoretical foundations of the problem.