Document Summarization via Convex-Concave Programming

Document summarization is an important task in various areas where the goal is to select a few the most descriptive sentences from a given document as a succinct summary. Even without training data of human labeled summaries, there has been several interesting existing work in the literature that yields reasonable performance. In this paper, within the same unsupervised learning setup, we propose a more principled learning framework for the document summarization task. Specifically we formulate an optimization problem that expresses the requirements of both faithful preservation of the document contents and the summary length constraint. We circumvent the difficult integer programming originating from binary sentence selection via continuous relaxation and the low entropy penalization. We also suggest an efficient convex-concave optimization solver algorithm that guarantees to improve the original objective at every iteration. For several document datasets, we demonstrate that the proposed learning algorithm significantly outperforms the existing approaches.