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On the Monotonization of a Training Set
Russian Academy of Sciences.
2010 (English)In: Computational Mathematics and Mathematical Physics, ISSN 0965-5425, Vol. 50, no 7, 1260-1266 p.Article in journal (Refereed) Published
Abstract [en]

The problem of finding a maximal subsample in a training sample consisting of the pairs “object-answer” that does not violate monotonicity constraints is considered. It is proved that this problem is NP-hard and that it is equivalent to the problem of finding a maximum independent set in special directed graphs. Practically important cases in which a partial order specified on the set of answers is a complete order or has dimension two are considered in detail. It is shown that the second case is reduced to the maximization of a quadratic convex function on a convex set. For this case, an approximate polynomial algorithm based on linear programming theory is proposed.

Place, publisher, year, edition, pages
Berlin: Springer , 2010. Vol. 50, no 7, 1260-1266 p.
National Category
Computer Science
URN: urn:nbn:se:liu:diva-63679DOI: 10.1134/S0965542510070146OAI: diva2:382146
Available from: 2010-12-29 Created: 2010-12-29 Last updated: 2011-06-21

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Takhanov, Rustem
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Computational Mathematics and Mathematical Physics
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