  This paper considers extractive summarisation in a comparative setting: given
two or more document groups (e.g., separated by publication time), the goal is
to select a small number of documents that are representative of each group,
and also maximally distinguishable from other groups. We formulate a set of new
objective functions for this problem that connect recent literature on document
summarisation, interpretable machine learning, and data subset selection. In
particular, by casting the problem as a binary classification amongst different
groups, we derive objectives based on the notion of maximum mean discrepancy,
as well as a simple yet effective gradient-based optimisation strategy. Our new
formulation allows scalable evaluations of comparative summarisation as a
classification task, both automatically and via crowd-sourcing. To this end, we
evaluate comparative summarisation methods on a newly curated collection of
controversial news topics over 13 months. We observe that gradient-based
optimisation outperforms discrete and baseline approaches in 14 out of 24
different automatic evaluation settings. In crowd-sourced evaluations,
summaries from gradient optimisation elicit 7% more accurate classification
from human workers than discrete optimisation. Our result contrasts with recent
literature on submodular data subset selection that favours discrete
optimisation. We posit that our formulation of comparative summarisation will
prove useful in a diverse range of use cases such as comparing content sources,
authors, related topics, or distinct view points.
