Solution stability in linear programming relaxations: Graph partitioning and unsupervised learning

Proceedings of the 26th International Conference On Machine Learning, ICML 2009

Volumn , Issue , 2009, Pages 769-776

  Nowozin, Sebastian ^a   Jegelka, Stefanie ^a  

^a MAX PLANCK INSTITUTE FOR BIOLOGICAL CYBERNETICS   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BENCH-MARK PROBLEMS; CLUSTERING AGGREGATION; CLUSTERING PROBLEMS; COMBINATORIAL OPTIMIZATION PROBLEMS; CORRELATION CLUSTERING; GRAPH PARTITIONING; LARGE CLASS; LINEAR PROGRAMMING RELAXATION; MACHINE-LEARNING; OPTIMAL SOLUTIONS; OPTIMIZATION PROBLEMS; RELATIVE PERFORMANCE; SOLUTION STABILITY;

COMBINATORIAL OPTIMIZATION; DYNAMIC PROGRAMMING; LINEAR PROGRAMMING; LINEARIZATION; ROBOT LEARNING; STABILITY;

EDUCATION;

EID: 71149085558     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (22)

1. Bansal, N., Blum, A., & Chawla, S. (2002). Correlation clustering. Foundations of Computer Science (FOCS'2002) (pp. 238-247). IEEE.
2. Bertsimas, D., & Tsitsiklis, J. N. (1997). Introduction to linear optimization. Athena Scientific, Massachusetts.
3. Brandes, U., Delling, D., Gaertler, M., Görke, R., Hoefer, M., Nikoloski, Z., & Wagner, D. (2008). On modularity clustering. IEEE Trans. Knowl. Data Eng, 20, 172-188.
4. Chopra, S., & Rao, M. R. (1993). The partition problem. Math. Program, 59, 87-115.
5. Demaine, E. D., Emanuel, D., Fiat, A., & Immorlica, N. (2006). Correlation clustering in general weighted graphs. Theor. Comput. Sci, 361, 172-187.
6. Deza, M. M., Grötschel, M., & Laurent, M. (1992). Clique-web facets for multicut polytopes. Mathematics of Operations Research, 17, 981-1000.
7. Deza, M. M., & Laurent, M. (1997). Geometry of cuts and metrics. Springer.
8. Emanuel, D., & Fiat, A. (2003). Correlation clustering - minimizing disagreements on arbitrary weighted graphs. Eur. Symp. Alg. (pp. 208-220). Springer.
9. Finley, T., & Joachims, T. (2005). Supervised clustering with support vector machines. Intl. Conf. Mach. Learn. (pp. 217-224). ACM.
10. Gaertler, M., Görke, R., & Wagner, D. (2007). Significance-driven graph clustering. Algorithmic Aspects in Information and Management. Springer.
11. Gionis, A., Mannila, H., & Tsaparas, P. (2007). Clustering aggregation. Trans. on Know. Discovery from Data, 1.
12. Grötschel, M., & Wakabayashi, Y. (1989). A cutting plane algorithm for a clustering problem. Math. Prog., 45, 59-96.
13. Grötschel, M., & Wakabayashi, Y. (1990). Facets of the clique partitioning polytope. Math. Prog., 47.
14. Jansen, B., Jong, J., Roos, C., & Terlaky, T. (1997). Sensitivity analysis in linear programming: Just be careful! European Journal of Operational Research, 101, 15-28.
15. Joachims, T., & Hopcroft, J. E. (2005). Error bounds for correlation clustering. Intl. Conf. Mach. Learn. (pp. 385-392). ACM.
16. Kernighan, B. W., & Lin, S. (1970). An efficient heuristic procedure for partitioning graphs. The Bell System Technical Journal, 291-307.
17. Kilmç-Karzan, F., Toriello, A., Ahmed, S., Nemhauser, G., & Savelsbergh, M. (2007). Approximating the stability region for binary mixed-integer programs (Technical Report). Gatech.
18. Newman, M. (2004). Analysis of weighted networks (Technical Report). Cornell University.
19. Newman, M. E. J., & Girvan, M. (2004). Finding and evaluating community structure in networks. Physical Review E, 69.
20. Rand, W. M. (1971). Objective criteria for the evaluation of clustering methods. American Statistical Association Journal, 66, 846-850.
21. Schrijver, A. (1998). Theory of linear and integer programming. John Wiley & Sons.
22. Wolsey, L. A. (1998). Integer programming. John Wiley.