![](bg6.png)
purpose of these methods is to reduce the matrix di-
mensionality, the resulted model will be more effi-
cient.
6 CONCLUSIONS AND FUTURE
WORK
In this paper we present a linear programming model
for the problem of extractive summarization. We rep-
resent the document as a sentence-term matrix whose
entries contain term count values and view this matrix
as a set of intersecting hyperplanes. Every possible
summary of a document is represented as an intersec-
tion of two or more hyperlanes, and one additional
constraint is used to limit the number of terms used in
a summary. We consider the summary to be the best
if term frequency is preserved during summarization,
and in this case the summarization problem translates
into a problem of finding a point on a convexpolytope
(defined by linear inequalities) which is the closest to
the hyperplane describing overall term frequencies in
the document.
Linear programming problem can be solved in
polynomial time (see (Karmarkar, 1984), (Khachiyan,
1996)). Numerous packages and applications are
available, such as (Berkelaar, 1999), (Makhorin,
2000) etc. In future research, we plan to implement
and test our approach, as in unsupervised as in super-
vised learning. Also, we’d like to extend our model to
query-based summarization by adapting the distance
function and apply our text representation model to
such text mining tasks like text clustering and text cat-
egorization.
ACKNOWLEDGEMENTS
The authors thank Ruvim Lipyansky for ideas that led
to development of their approach.
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