We propose a novel probabilistic approach to multilevel clustering problems
based on composite transportation distance, which is a variant of
transportation distance where the underlying metric is Kullback-Leibler
divergence. Our method involves solving a joint optimization problem over
spaces of probability measures to simultaneously discover grouping structures
within groups and among groups. By exploiting the connection of our method to
the problem of finding composite transportation barycenters, we develop fast
and efficient optimization algorithms even for potentially large-scale
multilevel datasets. Finally, we present experimental results with both
synthetic and real data to demonstrate the efficiency and scalability of the
proposed approach.Comment: 25 pages, 3 figure