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LP-Based Pivoting Algorithm for Higher-Order Correlation Clustering

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Computing and Combinatorics (COCOON 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10976))

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Abstract

Correlation clustering is an approach for clustering a set of objects from given pairwise information. In this approach, the given pairwise information is usually represented by an undirected graph with nodes corresponding to the objects, where each edge in the graph is assigned a nonnegative weight, and either the positive or negative label. Then, a clustering is obtained by solving an optimization problem of finding a partition of the node set that minimizes the disagreement or maximizes the agreement with the pairwise information. In this paper, we extend correlation clustering with disagreement minimization to deal with higher-order relationships represented by hypergraphs. We give two pivoting algorithms based on a linear programming relaxation of the problem. One achieves an \(O(k \log n)\)-approximation, where n is the number of nodes and k is the maximum size of hyperedges with the negative labels. This algorithm can be applied to any hyperedges with arbitrary weights. The other is an O(r)-approximation for complete r-partite hypergraphs with uniform weights. This type of hypergraphs arise from the coclustering setting of correlation clustering.

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References

  1. Ailon, N., Avigdor-Elgrabli, N., Liberty, E., van Zuylen, A.: Improved approximation algorithms for bipartite correlation clustering. SIAM J. Comput. 41(5), 1110–1121 (2012)

    Article  MathSciNet  Google Scholar 

  2. Amit, N.: The bicluster graph editing problem. Master thesis, Tel Aviv University (2004)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  4. Ben-Dor, A., Shamir, R., Yakhini, Z.: Clustering gene expression patterns. J. Comput. Biol. 6(3/4), 281–297 (1999)

    Article  Google Scholar 

  5. Bisson, G., Hussain, S.F.: Chi-sim: a new similarity measure for the co-clustering task. In: Proceedings of the Seventh ICMLA, pp. 211–217 (2008)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  7. Chawla, S., Krauthgamer, R., Kumar, R., Rabani, Y., Sivakumar, D.: On the hardness of approximating multicut and sparsest-cut. Comput. Complex. 15(2), 94–114 (2006)

    Article  MathSciNet  Google Scholar 

  8. Chawla, S., Makarychev, K., Schramm, T., Yaroslavtsev, G.: Near optimal LP rounding algorithm for correlation clustering on complete and complete k-partite graphs. In: Proceedings of the ACM STOC, pp. 219–228 (2015)

    Google Scholar 

  9. Chen, X., Ritter, A., Gupta, A., Mitchell, T.M.: Sense discovery via co-clustering on images and text. In: Proceedings IEEE CVPR, pp. 5298–5306 (2015)

    Google Scholar 

  10. Cheng, Y., Church, G.M.: Biclustering of expression data. In: Proceedings of the Eighth International Conference on Intelligent Systems for Molecular Biology, pp. 93–103 (2000)

    Google Scholar 

  11. Cohen, W.W., Richman, J.: Learning to match and cluster large high-dimensional data sets for data integration. In: Proceedings of the Eighth ACM SIGKDD, pp. 475–480 (2002)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  13. Dhillon, I.S.: Co-clustering documents and words using bipartite spectral graph partitioning. In: Proceedings of the Seventh ACM SIGKDD, pp. 269–274 (2001)

    Google Scholar 

  14. Dhillon, I.S., Mallela, S., Modha, D.S.: Information-theoretic co-clustering. In: Proceedings of the Ninth ACM SIGKDD, pp. 89–98 (2003)

    Google Scholar 

  15. Filkov, V., Skiena, S.: Integrating microarray data by consensus clustering. In: Proceedings of the 15th IEEE International Conference on Tools with Artificial Intelligence, pp. 418–425 (2003)

    Google Scholar 

  16. Hartigan, J.A.: Direct clustering of a data matrix. J. Am. Stat. Assoc. 67(337), 123–129 (1972)

    Article  Google Scholar 

  17. Hatano, D., Fukunaga, T., Kawarabayashi, K.: Scalable algorithm for higher-order co-clustering via random sampling. In: Proceedings of the Thirty-First AAAI, pp. 1992–1999 (2017)

    Google Scholar 

  18. Hussain, S.F., Bisson, G., Grimal, C.: An improved co-similarity measure for document clustering. In: Proceedings of the Ninth ICMLA, pp. 190–197 (2010)

    Google Scholar 

  19. Kappes, J.H., Speth, M., Reinelt, G., Schnörr, C.: Higher-order segmentation via multicuts. Comput. Vis. Image Underst. 143, 104–119 (2016)

    Article  Google Scholar 

  20. Kim, S., Nowozin, S., Kohli, P., Yoo, C.D.: Higher-order correlation clustering for image segmentation. In: Proceedings of the 25th NIPS, pp. 1530–1538 (2011)

    Google Scholar 

  21. Kim, S., Yoo, C.D., Nowozin, S., Kohli, P.: Image segmentation using higher-order correlation clustering. IEEE Trans. Pattern Anal. Mach. Intell. 36(9), 1761–1774 (2014)

    Article  Google Scholar 

  22. Madeira, S.C., Teixeira, M.C., Sá-Correia, I., Oliveira, A.L.: Identification of regulatory modules in time series gene expression data using a linear time biclustering algorithm. IEEE/ACM Trans. Comput. Biol. Bioinform. 7(1), 153–165 (2010)

    Article  Google Scholar 

  23. McCallum, A., Wellner, B.: Toward conditional models of identity uncertainty with application to proper noun coreference. In: Proceedings of the IIWeb, pp. 79–84 (2003)

    Google Scholar 

  24. Papalexakis, E.E., Sidiropoulos, N.D., Bro, R.: From K-means to higher-way co-clustering: multilinear decomposition with sparse latent factors. IEEE Trans. Sig. Process. 61(2), 493–506 (2013)

    Article  Google Scholar 

  25. Peng, W., Li, T.: Temporal relation co-clustering on directional social network and author-topic evolution. Knowl. Inf. Syst. 26(3), 467–486 (2011)

    Article  MathSciNet  Google Scholar 

  26. Shan, H., Banerjee, A.: Bayesian co-clustering. In: Proceedings of the 8th IEEE ICDM, pp. 530–539 (2008)

    Google Scholar 

  27. Zha, H., He, X., Ding, C.H.Q., Gu, M., Simon, H.D.: Bipartite graph partitioning and data clustering. In: Proceedings of the ACM CIKM, pp. 25–32 (2001)

    Google Scholar 

  28. Zhao, L., Zaki, M.J.: TriCluster: an effective algorithm for mining coherent clusters in 3D microarray data. In: Proceedings of the ACM SIGMOD, pp. 694–705 (2005)

    Google Scholar 

  29. Zhu, Y., Yang, H., He, J.: Co-clustering based dual prediction for cargo pricing optimization. In: Proceedings of the 21th ACM SIGKDD, pp. 1583–1592 (2015)

    Google Scholar 

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Acknowledgments

The author is grateful to anonymous referees for their comments. This study was supported by JSPS KAKENHI Grant Number JP17K00040.

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Correspondence to Takuro Fukunaga .

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Fukunaga, T. (2018). LP-Based Pivoting Algorithm for Higher-Order Correlation Clustering. In: Wang, L., Zhu, D. (eds) Computing and Combinatorics. COCOON 2018. Lecture Notes in Computer Science(), vol 10976. Springer, Cham. https://doi.org/10.1007/978-3-319-94776-1_5

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  • DOI: https://doi.org/10.1007/978-3-319-94776-1_5

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  • Online ISBN: 978-3-319-94776-1

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