Abstract
The paper describes a convex optimization formulation of the extractive text summarization problem and a simple and scalable algorithm to solve it. The optimization program is constructed as a convex relaxation of an intuitive but computationally hard integer programming problem. The objective function is highly symmetric, being invariant under unitary transformations of the text representations. Another key idea is to replace the constraint on the number of sentences in the summary with a convex surrogate. For solving the program we have designed a specific projected gradient descent algorithm and analyzed its performance in terms of execution time and quality of the approximation. Using the datasets DUC 2005 and Cornell Newsroom Summarization Dataset, we have shown empirically that the algorithm can provide competitive results for single document summarization and multi-document query-based summarization. On the Cornell Newsroom Summarization Dataset, it ranked second among the unsupervised methods tested. For the more challenging task of multi-document query-based summarization, the method was tested on the DUC 2005 Dataset. Our algorithm surpassed the other reported methods with respect to the ROUGE-SU4 metric, and it was at less than 0.01 from the top performing algorithms with respect to ROUGE-1 and ROUGE-2 metrics.
Highlights
The process of providing a concise, fluent, and accurate summary starting from a text document or a group of documents is called text summarization [1]
We proceed to evaluate the method on two different tasks: single document summarization and query-based multi-document summarization
We have proposed a new algorithm for extractive text summarization based on some simple and intuitive ideas, and we have tried to establish its properties and performance
Summary
The process of providing a concise, fluent, and accurate summary starting from a text document or a group of documents is called text summarization [1]. One method to generate a summary is by extracting and recombining the most relevant parts from the original text or texts This process is known as extractive summarization and our work is focused on this problem. The method described in this paper is based on minimizing a convex function subject to some constraints and on the properties of the l1 norm [3]. The properties of this norm are well known and it has many applications in signal processing (compressive sampling [4]) and statistics/machine learning (LASSO regression [5]). For the basic notions from convex optimization and signal processing used in this paper we refer the reader to Appendix C and references therein
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