# Polytope Model for Extractive Summarization

### Marina Litvak, Natalia Vanetik

#### Abstract

The problem of text summarization for a collection of documents is defined as the problem of selecting a small subset of sentences so that the contents and meaning of the original document set are preserved in the best possible way. In this paper we present a linear model for the problem of text summarization, where we strive to obtain a summary that preserves the information coverage as much as possible in comparison to the original document set. We construct a system of linear inequalities that describes the given document set and its possible summaries and translate the problem of finding the best summary to the problem of finding the point on a convex polytope closest to the given hyperplane. This re-formulated problem can be solved efficiently with the help of quadratic programming.

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#### Paper Citation

#### in Harvard Style

Litvak M. and Vanetik N. (2012). **Polytope Model for Extractive Summarization** . In *Proceedings of the International Conference on Knowledge Discovery and Information Retrieval - Volume 1: KDIR, (IC3K 2012)* ISBN 978-989-8565-29-7, pages 281-286. DOI: 10.5220/0004170902810286

#### in Bibtex Style

@conference{kdir12,

author={Marina Litvak and Natalia Vanetik},

title={Polytope Model for Extractive Summarization},

booktitle={Proceedings of the International Conference on Knowledge Discovery and Information Retrieval - Volume 1: KDIR, (IC3K 2012)},

year={2012},

pages={281-286},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004170902810286},

isbn={978-989-8565-29-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Knowledge Discovery and Information Retrieval - Volume 1: KDIR, (IC3K 2012)

TI - Polytope Model for Extractive Summarization

SN - 978-989-8565-29-7

AU - Litvak M.

AU - Vanetik N.

PY - 2012

SP - 281

EP - 286

DO - 10.5220/0004170902810286