K-Partitioning with Imprecise Probabilistic Edges

Partitioning a set of elements into disjoint subsets is a common problem in unsupervised learning (clustering) as well as in networks (e.g., social, ecological) where one wants to find heterogeneous subgroups such that the elements within each subgroup are homogeneous. In this paper, we are concerned with the case where we imprecisely know the probability that two elements should belong to the same partition, and where we want to search the set of most probable partitions. We study the corresponding algorithmic problem on graphs, showing that it is difficult, and propose heuristic procedures that we test on data sets.