Quantitative Biology

, Volume 6, Issue 1, pp 56–67 | Cite as

Biclustering by sparse canonical correlation analysis

  • Harold Pimentel
  • Zhiyue Hu
  • Haiyan HuangEmail author
Research Article



Developing appropriate computational tools to distill biological insights from large-scale gene expression data has been an important part of systems biology. Considering that gene relationships may change or only exist in a subset of collected samples, biclustering that involves clustering both genes and samples has become increasingly important, especially when the samples are pooled from a wide range of experimental conditions.


In this paper, we introduce a new biclustering algorithm to find subsets of genomic expression features (EFs) (e.g., genes, isoforms, exon inclusion) that show strong “group interactions” under certain subsets of samples. Group interactions are defined by strong partial correlations, or equivalently, conditional dependencies between EFs after removing the influences of a set of other functionally related EFs. Our new biclustering method, named SCCA-BC, extends an existing method for group interaction inference, which is based on sparse canonical correlation analysis (SCCA) coupled with repeated random partitioning of the gene expression data set.


SCCA-BC gives sensible results on real data sets and outperforms most existing methods in simulations. Software is available at


SCCA-BC seems to work in numerous conditions and the results seem promising for future extensions. SCCA-BC has the ability to find different types of bicluster patterns, and it is especially advantageous in identifying a bicluster whose elements share the same progressive and multivariate normal distribution with a dense covariance matrix.


biclustering SCCA gene clusters 


  1. 1.
    Eisen, M. B., Spellman, P. T., Brown, P. O. and Botstein, D. (1998) Cluster analysis and display of genome-wide expression patterns. Proc. Natl. Acad. Sci. USA, 95, 14863–14868CrossRefPubMedPubMedCentralGoogle Scholar
  2. 2.
    Lazzeroni, L. and Owen, A. (2002) Plaid models for gene expression data. Stat. Sin., 12, 61–86Google Scholar
  3. 3.
    Kluger, Y., Basri, R., Chang, J. T. and Gerstein, M. (2003) Spectral biclustering of microarray data: coclustering genes and conditions. Genome Res., 13, 703–716CrossRefPubMedPubMedCentralGoogle Scholar
  4. 4.
    Bhattacharya, A. and De, R. K. (2009) Bi-correlation clustering algorithm for determining a set of co-regulated genes. Bioinformatics, 25, 2795–2801CrossRefPubMedGoogle Scholar
  5. 5.
    Nepomuceno, J. A., Troncoso, A. and Aguilar-Ruiz, J. S. (2011) Biclustering of gene expression data by correlation-based scatter search. BioData Min., 4, 3CrossRefPubMedPubMedCentralGoogle Scholar
  6. 6.
    Gao, Q., Ho, C., Jia, Y., Li, J. J. and Huang, H. (2012) Biclustering of linear patterns in gene expression data. J. Comput. Biol., 19, 619–631CrossRefPubMedPubMedCentralGoogle Scholar
  7. 7.
    Ben-Dor, A., Chor, B., Karp, R. and Yakhini, Z. (2003) Discovering local structure in gene expression data: the orderpreserving submatrix problem. J. Comput. Biol., 10, 373–384CrossRefPubMedGoogle Scholar
  8. 8.
    Liu, J. and Wang, W. (2003) Op-cluster: Clustering by tendency in high dimensional space. In Third IEEE International Conference on Data Mining, 2003. ICDM 2003, pp. 187–194 IEEEGoogle Scholar
  9. 9.
    Wang, Y. X. R., Jiang, K., Feldman, L. J., Bickel, P. J., and Huang, H. (2015) Inferring gene-gene interactions and functional modules using sparse canonical correlation analysis. Ann. Appl. Stat. 9, 300–323CrossRefGoogle Scholar
  10. 10.
    Tan, K. M. and Witten, D. M. (2014) Sparse biclustering of transposable data. J. Comput. Graph. Stat., 23, 985–1008CrossRefPubMedPubMedCentralGoogle Scholar
  11. 11.
    Turner, H., Bailey, T. and Krzanowski, W. (2005) Improved biclustering of microarray data demonstrated through systematic performance tests. Comput. Stat. Data Anal., 48, 235–254CrossRefGoogle Scholar
  12. 12.
    Lee, M., Shen, H., Huang, J. Z. and Marron, J. S. (2010) Biclustering via sparse singular value decomposition. Biometrics, 66, 1087–1095CrossRefPubMedGoogle Scholar
  13. 13.
    Prelić, A., Bleuler, S., Zimmermann, P., Wille, A., Bhlmann, P., Gruissem, W., Hennig, L., Thiele, L. and Zitzler, E. (2006) A systematic comparison and evaluation of biclustering methods for gene expression data. Bioinformatics, 22, 1122–1129CrossRefPubMedGoogle Scholar
  14. 14.
    Higham, N. J. (2002) Computing the nearest correlation matrix–a problem from finance. IMA J. Numer. Anal., 22, 329–343CrossRefGoogle Scholar
  15. 15.
    St Johnston, D. (2002) The art and design of genetic screens: Drosophila melanogaster. Nat. Rev. Genet., 3, 176–188CrossRefGoogle Scholar
  16. 16.
    Jorgensen, E. M. and Mango, S. E. (2002) The art and design of genetic screens: Caenorhabditis elegans. Nat. Rev.Genet., 3, 356–369CrossRefPubMedGoogle Scholar
  17. 17.
    Brown, J. B., Boley, N., Eisman, R., May, G. E., Stoiber, M. H., Duff, M. O., Booth, B. W., Wen, J., Park, S., Suzuki, A. M., et al. (2014) Diversity and dynamics of the Drosophila transcriptome. Nature, 512, 393–399CrossRefPubMedPubMedCentralGoogle Scholar
  18. 18.
    Hotelling, H. (1936) Relations between two sets of variates. Biometrika, 28, 321–377CrossRefGoogle Scholar
  19. 19.
    Lee, W., Lee, D., Lee, Y. and Pawitan, Y. (2011) Sparse canonical covariance analysis for high-throughput data. Stat. Appl. Genet. Mol. Biol., 10Google Scholar
  20. 20.
    Tibshirani, R., Walther, G. and Hastie, T. (2001) Estimating the number of clusters in a dataset via the gap statistic. J. R. Stat. Soc. B, 63, 411–423CrossRefGoogle Scholar
  21. 21.
    Anderson, T. W. (1958) An Introduction to Multivariate Statistical Analysis. New York: WileyGoogle Scholar
  22. 22.
    Tibshirani, R. (1996) Regression shrinkage and selection via the lasso. J. R. Stat. Soc. B, 267–288Google Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of CaliforniaBerkeleyUSA
  2. 2.Department of StatisticsUniversity of CaliforniaBerkeleyUSA

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