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  Solution Stability in Linear Programming Relaxations: Graph Partitioning and Unsupervised Learning

Nowozin, S., & Jegelka, S. (2009). Solution Stability in Linear Programming Relaxations: Graph Partitioning and Unsupervised Learning. In A. Danyluk, L. Bottou, & M. Littman (Eds.), ICML '09: Proceedings of the 26th Annual International Conference on Machine Learning (pp. 769-776). New York, NY, USA: ACM Press.

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 Creators:
Nowozin, S1, 2, Author              
Jegelka, S1, 2, Author              
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: We propose a new method to quantify the solution stability of a large class of combinatorial optimization problems arising in machine learning. As practical example we apply the method to correlation clustering, clustering aggregation, modularity clustering, and relative performance significance clustering. Our method is extensively motivated by the idea of linear programming relaxations. We prove that when a relaxation is used to solve the original clustering problem, then the solution stability calculated by our method is conservative, that is, it never overestimates the solution stability of the true, unrelaxed problem. We also demonstrate how our method can be used to compute the entire path of optimal solutions as the optimization problem is increasingly perturbed. Experimentally, our method is shown to perform well on a number of benchmark problems.

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 Dates: 2009-06
 Publication Status: Published in print
 Pages: -
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 Rev. Type: -
 Identifiers: DOI: 10.1145/1553374.1553473
BibTex Citekey: 5878
 Degree: -

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Title: 26th International Conference on Machine Learning (ICML 2009)
Place of Event: Montreal, Canada
Start-/End Date: 2009-06-14 - 2009-06-18

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Title: ICML '09: Proceedings of the 26th Annual International Conference on Machine Learning
Source Genre: Proceedings
 Creator(s):
Danyluk, A, Editor
Bottou, L, Editor
Littman, M, Editor
Affiliations:
-
Publ. Info: New York, NY, USA : ACM Press
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 769 - 776 Identifier: ISBN: 978-1-60558-516-1

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Title: ACM International Conference Proceeding Series
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Pages: - Volume / Issue: 382 Sequence Number: - Start / End Page: - Identifier: -