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Theory of linear and integer programming
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Facets of the clique partitioning polytope
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Mathematics of Operations Research
Mathematical Programming: Series A and B
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Introduction to Linear Optimization
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ICML '05 Proceedings of the 22nd international conference on Machine learning
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ICML '05 Proceedings of the 22nd international conference on Machine learning
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IEEE Transactions on Knowledge and Data Engineering
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Foundations and Trends® in Computer Graphics and Vision
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ACCV'12 Proceedings of the 11th Asian conference on Computer Vision - Volume Part I
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SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition
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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.