  Existing graph-based methods for extractive document summarization represent
sentences of a corpus as the nodes of a graph or a hypergraph in which edges
depict relationships of lexical similarity between sentences. Such approaches
fail to capture semantic similarities between sentences when they express a
similar information but have few words in common and are thus lexically
dissimilar. To overcome this issue, we propose to extract semantic similarities
based on topical representations of sentences. Inspired by the Hierarchical
Dirichlet Process, we propose a probabilistic topic model in order to infer
topic distributions of sentences. As each topic defines a semantic connection
among a group of sentences with a certain degree of membership for each
sentence, we propose a fuzzy hypergraph model in which nodes are sentences and
fuzzy hyperedges are topics. To produce an informative summary, we extract a
set of sentences from the corpus by simultaneously maximizing their relevance
to a user-defined query, their centrality in the fuzzy hypergraph and their
coverage of topics present in the corpus. We formulate a polynomial time
algorithm building on the theory of submodular functions to solve the
associated optimization problem. A thorough comparative analysis with other
graph-based summarization systems is included in the paper. Our obtained
results show the superiority of our method in terms of content coverage of the
summaries.
