  Extractive text summarisation aims to select salient sentences from a
document to form a short yet informative summary. While learning-based methods
have achieved promising results, they have several limitations, such as
dependence on expensive training and lack of interpretability. Therefore, in
this paper, we propose a novel non-learning-based method by for the first time
formulating text summarisation as an Optimal Transport (OT) problem, namely
Optimal Transport Extractive Summariser (OTExtSum). Optimal sentence extraction
is conceptualised as obtaining an optimal summary that minimises the
transportation cost to a given document regarding their semantic distributions.
Such a cost is defined by the Wasserstein distance and used to measure the
summary's semantic coverage of the original document. Comprehensive experiments
on four challenging and widely used datasets - MultiNews, PubMed, BillSum, and
CNN/DM demonstrate that our proposed method outperforms the state-of-the-art
non-learning-based methods and several recent learning-based methods in terms
of the ROUGE metric.
