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A Comparative Study of Local Search Algorithms for Correlation Clustering

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Pattern Recognition (GCPR 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10496))

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Abstract

This paper empirically compares four local search algorithms for correlation clustering by applying these to a variety of instances of the correlation clustering problem for the tasks of image segmentation, hand-written digit classification and social network analysis. Although the local search algorithms establish neither lower bounds nor approximation certificates, they converge monotonously to a fixpoint, offering a feasible solution at any time. For some algorithms, the time of convergence is affordable for all instances we consider. This finding encourages a broader application of correlation clustering, especially in settings where the number of clusters is not known and needs to be estimated from data.

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Notes

  1. 1.

    http://caffe.berkeleyvision.org/gathered/examples/mnist.html.

References

  1. Alush, A., Goldberger, J.: Ensemble segmentation using efficient integer linear programming. TPAMI 34(10), 1966–1977 (2012)

    Article  Google Scholar 

  2. Alush, A., Goldberger, J.: Hierarchical image segmentation using correlation clustering. IEEE Trans. Neural Netw. Learn. Syst. PP(99), 1–10 (2015)

    Google Scholar 

  3. Andres, B., Kappes, J.H., Beier, T., Köthe, U., Hamprecht, F.A.: Probabilistic image segmentation with closedness constraints. In: ICCV (2011)

    Google Scholar 

  4. Andres, B., Kröger, T., Briggman, K.L., Denk, W., Korogod, N., Knott, G., Köthe, U., Hamprecht, F.A.: Globally optimal closed-surface segmentation for connectomics. In: ECCV (2012)

    Google Scholar 

  5. Bachrach, Y., Kohli, P., Kolmogorov, V., Zadimoghaddam, M.: Optimal coalition structure generation in cooperative graph games. In: AAAI (2013). http://www.aaai.org/ocs/index.php/AAAI/AAAI13/paper/view/6407/7071

  6. Bagon, S., Galun, M.: Large scale correlation clustering optimization. CoRR abs/1112.2903 (2011). http://arxiv.org/abs/1112.2903

  7. Bansal, N., Blum, A., Chawla, S.: Correlation clustering. Mach. Learn. 56(1–3), 89–113 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  8. Beier, T., Hamprecht, F.A., Kappes, J.H.: Fusion moves for correlation clustering. In: CVPR (2015)

    Google Scholar 

  9. Beier, T., Kröger, T., Kappes, J.H., Köthe, U., Hamprecht, F.A.: Cut, Glue & Cut: a fast, approximate solver for multicut partitioning. In: CVPR (2014)

    Google Scholar 

  10. Charikar, M., Guruswami, V., Wirth, A.: Clustering with qualitative information. J. Comput. Syst. Sci. 71(3), 360–383 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. Chopra, S., Rao, M.: The partition problem. Math. Program. 59(1–3), 87–115 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  12. Dahlhaus, E., Johnson, D.S., Papadimitriou, C.H., Seymour, P.D., Yannakakis, M.: The complexity of multiterminal cuts. SIAM J. Comput. 23, 864–894 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  13. Demaine, E.D., Emanuel, D., Fiat, A., Immorlica, N.: Correlation clustering in general weighted graphs. Theoret. Comput. Sci. 361(2–3), 172–187 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  14. Goldschmidt, O., Hochbaum, D.S.: A polynomial algorithm for the k-cut problem for fixed k. Math. Oper. Res. 19(1), 24–37 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  15. Grötschel, M., Wakabayashi, Y.: A cutting plane algorithm for a clustering problem. Math. Program. 45(1), 59–96 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  16. Horňáková, A., Lange, J.H., Andres, B.: Analysis and optimization of graph decompositions by lifted multicuts. In: ICML (Forthcoming) (2017)

    Google Scholar 

  17. Jia, Y., Shelhamer, E., Donahue, J., Karayev, S., Long, J., Girshick, R., Guadarrama, S., Darrell, T.: Caffe: convolutional architecture for fast feature embedding (2014). arXiv preprint arXiv:1408.5093

  18. Kappes, J.H., Andres, B., Hamprecht, F.A., Schnörr, C., Nowozin, S., Batra, D., Kim, S., Kausler, B.X., Kröger, T., Lellmann, J., Komodakis, N., Savchynskyy, B., Rother, C.: A comparative study of modern inference techniques for structured discrete energy minimization problems. Int. J. Comput. Vis. 115(2), 155–184 (2015)

    Article  MathSciNet  Google Scholar 

  19. Kappes, J.H., Speth, M., Andres, B., Reinelt, G., Schnörr, C.: Globally optimal image partitioning by multicuts. In: EMMCVPR (2011)

    Google Scholar 

  20. Kappes, J.H., Speth, M., Reinelt, G., Schnörr, C.: Higher-order segmentation via multicuts. Comput. Vis. Image Underst. 143, 104–119 (2015)

    Article  Google Scholar 

  21. Kappes, J.H., Swoboda, P., Savchynskyy, B., Hazan, T., Schnörr, C.: Probabilistic correlation clustering and image partitioning using perturbed multicuts. In: Scale Space and Variational Methods in Computer Vision (2015)

    Google Scholar 

  22. Kernighan, B.W., Lin, S.: An efficient heuristic procedure for partitioning graphs. Bell Syst. Tech. J. 49, 291–307 (1970)

    Article  MATH  Google Scholar 

  23. Keuper, M., Andres, B., Brox, T.: Motion trajectory segmentation via minimum cost multicuts. In: ICCV (2015)

    Google Scholar 

  24. Keuper, M., Levinkov, E., Bonneel, N., Lavoué, G., Brox, T., Andres, B.: Efficient decomposition of image and mesh graphs by lifted multicuts. In: International Conference on Computer Vision (2015)

    Google Scholar 

  25. Kim, S., Nowozin, S., Kohli, P., Yoo, C.: Higher-order correlation clustering for image segmentation. In: NIPS (2011)

    Google Scholar 

  26. Kim, S., Yoo, C., Nowozin, S., Kohli, P.: Image segmentation using higher-order correlation clustering. TPAMI 36, 1761–1774 (2014)

    Article  Google Scholar 

  27. Klein, P.N., Mathieu, C., Zhou, H.: Correlation clustering and two-edge-connected augmentation for planar graphs. In: Mayr, E.W., Ollinger, N. (eds.) 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics, vol. 30, pp. 554–567. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl (2015)

    Google Scholar 

  28. Knott, G., Marchman, H., Wall, D., Lich, B.: Serial section scanning electron microscopy of adult brain tissue using focused ion beam milling. J. Neurosci. 28(12), 2959–2964 (2008)

    Article  Google Scholar 

  29. LeCun, Y., Bottou, L., Bengio, Y., Haffner, P.: Gradient-based learning applied to document recognition. Proc. IEEE 86(11), 2278–2324 (1998)

    Article  Google Scholar 

  30. Lecun, Y., Cortes, C.: The MNIST database of handwritten digits. http://yann.lecun.com/exdb/mnist/

  31. Leskovec, J., Huttenlocher, D., Kleinberg, J.: Signed networks in social media. In: CHI (2010)

    Google Scholar 

  32. Martin, D., Fowlkes, C., Tal, D., Malik, J.: A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: Proceedings of the 8th International Conference on Computer Vision, vol. 2, pp. 416–423, July 2001

    Google Scholar 

  33. Meilă, M.: Comparing clusterings–an information based distance. J. Multivar. Anal. 98(5), 873–895 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  34. Nowozin, S., Jegelka, S.: Solution stability in linear programming relaxations: graph partitioning and unsupervised learning. In: ICML (2009)

    Google Scholar 

  35. Rother, C., Kolmogorov, V., Lempitsky, V., Szummer, M.: Optimizing binary MRFs via extended roof duality. In: CVPR (2007)

    Google Scholar 

  36. Schraudolph, N.N., Kamenetsky, D.: Efficient exact inference in planar ising models. In: NIPS (2009)

    Google Scholar 

  37. Voice, T., Polukarov, M., Jennings, N.R.: Coalition structure generation over graphs. J. Artif. Intell. Res. 45, 165–196 (2012)

    MathSciNet  MATH  Google Scholar 

  38. Yarkony, J.: Analyzing PlanarCC: demonstrating the equivalence of PlanarCC and the multi-cut LP relaxation. In: NIPS Workshop on Discrete Optimization (2014)

    Google Scholar 

  39. Yarkony, J., Ihler, A., Fowlkes, C.C.: Fast planar correlation clustering for image segmentation. In: ECCV (2012)

    Google Scholar 

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Authors and Affiliations

  1. Max Planck Institute for Informatics, Saarland Informatics Campus, Saarbrücken, Germany

    Evgeny Levinkov & Bjoern Andres

  2. Computer Vision Lab, Technische Universität Dresden, Dresden, Germany

    Alexander Kirillov

Authors
  1. Evgeny Levinkov
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  2. Alexander Kirillov
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  3. Bjoern Andres
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Correspondence to Bjoern Andres .

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Editors and Affiliations

  1. University of Basel, Basel, Switzerland

    Volker Roth

  2. University of Basel, Basel, Switzerland

    Thomas Vetter

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Levinkov, E., Kirillov, A., Andres, B. (2017). A Comparative Study of Local Search Algorithms for Correlation Clustering. In: Roth, V., Vetter, T. (eds) Pattern Recognition. GCPR 2017. Lecture Notes in Computer Science(), vol 10496. Springer, Cham. https://doi.org/10.1007/978-3-319-66709-6_9

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  • DOI: https://doi.org/10.1007/978-3-319-66709-6_9

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  • Online ISBN: 978-3-319-66709-6

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