Extractive Summarization by Maximizing Semantic Volume

The most successful approaches to extractive text summarization seek to maximize bigram coverage subject to a budget constraint. In this work, we propose instead to maximize semantic volume. We embed each sentence in a semantic space and construct a summary by choosing a subset of sentences whose convex hull maximizes volume in that space. We provide a greedy algorithm based on the Gram-Schmidt process to efficiently perform volume maximization. Our method outperforms the state-of-the-art summarization approaches on benchmark datasets.