Abstract
Jointly clustering the rows and the columns of large matrices, a.k.a. co-clustering, finds numerous applications in the real world such as collaborative filtering, market-basket and micro-array data analysis, graph clustering, etc. In this paper, we formulate an information-theoretic objective cost function to solve this problem, and develop a fast agglomerative algorithm to optimize this objective. Our algorithm rapidly finds highly similar clusters to be merged in an iterative fashion using Locality-Sensitive Hashing. Thanks to its bottom-up nature, it also enables the analysis of the cluster hierarchies. Finally, the number of row and column clusters are automatically determined without requiring the user to choose them. Our experiments on both real and synthetic datasets show that the proposed algorithm achieves high-quality clustering solutions and scales linearly with the input matrix size.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abdullah, A., Hussain, A.: A new biclustering technique based on crossing minimization. Neurocomputing 69(16-18), 1882–1896 (2006)
Agrawal, R., Gehrke, J., Gunopulos, D., Raghavan, P.: Automatic subspace clustering of high dimensional data. In: SIGMOD, pp. 94–105 (1998)
Agrawal, R., Imieliński, T., Swami, A.: Mining association rules between sets of items in large databases. SIGMOD 22(2), 207–216 (1993)
Akoglu, L., Tong, H., Meeder, B., Faloutsos, C.: Pics: Parameter-free identification of cohesive subgroups in large attributed graphs. In: SDM (2012)
Calders, T., Goethals, B.: Mining all non-derivable frequent itemsets. In: Elomaa, T., Mannila, H., Toivonen, H. (eds.) PKDD 2002. LNCS (LNAI), vol. 2431, pp. 74–86. Springer, Heidelberg (2002)
Chakrabarti, D.: AutoPart: Parameter-free graph partitioning and outlier detection. In: Boulicaut, J.-F., Esposito, F., Giannotti, F., Pedreschi, D. (eds.) PKDD 2004. LNCS (LNAI), vol. 3202, pp. 112–124. Springer, Heidelberg (2004)
Chakrabarti, D., Papadimitriou, S., Modha, D.S., Faloutsos, C.: Fully automatic cross-associations. In: ACM SIGKDD, pp. 79–88 (2004)
Deerwester, S., Dumais, S., Furnas, G., Landauer, T., Harshman, R.: Indexing by latent semantic analysis. JASI 41(6), 391–407 (1990)
Dhillon, I., Mallela, S., Modha, D.: Information- theoretic co-clustering. In: ACM SIGKDD (2003)
Fortunato, S., Barthélemy, M.: PNAS, 104(1), 36 (2007)
Gionis, A., Indyk, P., Motwani, R.: Similarity search in high dimensions via hashing. In: VLDB, pp. 518–529 (1999)
Gionis, A., Mannila, H., Seppänen, J.K.: Geometric and combinatorial tiles in 0-1 data. In: Boulicaut, J.-F., Esposito, F., Giannotti, F., Pedreschi, D. (eds.) PKDD 2004. LNCS (LNAI), vol. 3202, pp. 173–184. Springer, Heidelberg (2004)
Hamerly, G., Elkan, C.: Learning the k in k-means. In: NIPS (2003)
Han, J., Wang, J., Lu, Y., Tzvetkov, P.: Mining top-k frequent closed patterns without minimum support. In: ICDM, pp. 211–218 (2002)
Karypis, G., Han, E.-H., Kumar, V.: Chameleon: Hierarchical clustering using dynamic modeling. IEEE Computer 32(8) (1999)
Kriegel, H.-P., Kröger, P., Zimek, A.: Clustering high-dimensional data: A survey. TKDD 3(1), 1:1–1:58 (2009)
Kröger, P., Kriegel, H.-P., Kailing, K.: Density-connected subspace clustering for high-dimensional data. In: SDM (2004)
Manning, C.D., Raghavan, P., Schtze, H.: Introduction to Information Retrieval. Cambridge University Press (2008)
Mishra, N., Ron, D., Swaminathan, R.: On finding large conjunctive clusters. In: Schölkopf, B., Warmuth, M.K. (eds.) COLT/Kernel 2003. LNCS (LNAI), vol. 2777, pp. 448–462. Springer, Heidelberg (2003)
Newman, M.E.J.: Fast algorithm for detecting community structure in networks. Physical Review EÂ 69 (2004)
Ng, A.Y., Jordan, M.I., Weiss, Y.: On spectral clustering: Analysis and an algorithm. In: NIPS (2001)
Pan, J., Manocha, D.: Bi-level locality sensitive hashing for k-nearest neighbor computation. In: ICDE, pp. 378–389 (2012)
Pelleg, D., Moore, A.: X-means: Extending K-means with efficient estimation of the number of clusters. In: ICML (2000)
Reiss, D.J., Baliga, N.S., Bonneau, R.: Integrated biclustering of heterogeneous genome-wide datasets. BMC Bioinformatics 7, 280 (2006)
Rissanen, J.: A universal prior for integers and estimation by minimum description length. The Annals of Statistics 11(2), 416–431 (1983)
Satuluri, V., Parthasarathy, S.: Bayesian locality sensitive hashing for fast similarity search. PVLDB 5(5), 430–441 (2012)
Slonim, N., Tishby, N.: Agglomerative information bottleneck. In: NIPS (1999)
Sun, J., Faloutsos, C., Papadimitriou, S., Yu, P.S.: Graphscope: parameter-free mining of large time-evolving graphs. In: ACM SIGKDD, pp. 687–696 (2007)
Wang, Y., Parthasarathy, S., Tatikonda, S.: Locality sensitive outlier detection: A ranking driven approach. In: ICDE, pp. 410–421 (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Gao, T., Akoglu, L. (2014). Fast Information-Theoretic Agglomerative Co-clustering. In: Wang, H., Sharaf, M.A. (eds) Databases Theory and Applications. ADC 2014. Lecture Notes in Computer Science, vol 8506. Springer, Cham. https://doi.org/10.1007/978-3-319-08608-8_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-08608-8_13
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08607-1
Online ISBN: 978-3-319-08608-8
eBook Packages: Computer ScienceComputer Science (R0)