Biclustering by sparse canonical correlation analysis

Abstract

Background: 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 in-creasingly important, especially when the samples are pooled from a wide range of experimental conditions.

Methods: 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.

Results: SCCA-BC gives sensible results on real data sets and outperforms most existing methods in simulations. Software is available at https://github.com/pimentel/scca-bc.

Conclusions: 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.

Graphical abstract

Keywords

biclustering / SCCA / gene clusters

References

[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, 14863–14868

[2] Lazzeroni, L. and Owen, A. (2002) Plaid models for gene expression data. Stat. Sin., 12, 61–86

[3] Kluger, Y., Basri, R., Chang, J. T. and Gerstein, M. (2003) Spectral biclustering of microarray data: coclustering genes and conditions. Genome Res., 13, 703–716

[4] Bhattacharya, A. and De, R. K. (2009) Bi-correlation clustering algorithm for determining a set of co-regulated genes. Bioinformatics, 25, 2795–2801

[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, 3

[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, 619–631

[7] Ben-Dor, A., Chor, B., Karp, R. and Yakhini, Z. (2003) Discovering local structure in gene expression data: the order-preserving submatrix problem. J. Comput. Biol., 10, 373–384

[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 IEEE

[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, 300–323

[10] Tan, K. M. and Witten, D. M. (2014) Sparse biclustering of transposable data. J. Comput. Graph. Stat., 23, 985–1008

[11] Turner, H., Bailey, T. and Krzanowski, W. (2005) Improved biclustering of microarray data demonstrated through systematic performance tests. Comput. Stat. Data Anal., 48, 235–254

[12] Lee, M., Shen, H., Huang, J. Z. and Marron, J. S. (2010) Biclustering via sparse singular value decomposition. Biometrics, 66, 1087–1095

[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, 1122–1129

[14] Higham, N. J. (2002) Computing the nearest correlation matrix–a problem from finance. IMA J. Numer. Anal., 22, 329–343

[15] St Johnston, D. (2002) The art and design of genetic screens: Drosophila melanogaster. Nat. Rev. Genet., 3, 176–188

[16] Jorgensen, E. M. and Mango, S. E. (2002) The art and design of genetic screens: Caenorhabditis elegans. Nat. Rev.Genet., 3, 356–369

[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., (2014) Diversity and dynamics of the Drosophila transcriptome. Nature, 512, 393–399

[18] Hotelling, H. (1936) Relations between two sets of variates. Biometrika, 28, 321–377

[19] Lee, W., Lee, D., Lee, Y. and Pawitan, Y. (2011) Sparse canonical covariance analysis for high-throughput data. Stat. Appl. Genet. Mol. Biol., 10

[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, 411–423

[21] Anderson, T. W. (1958) An Introduction to Multivariate Statistical Analysis. New York: Wiley

[22] Tibshirani, R. (1996) Regression shrinkage and selection via the lasso. J. R. Stat. Soc. B, 267–288

ACKNOWLEDGEMENT

The work is partially supported by NSF DMS-1160319.

COMPLIANCE WITH ETHICS GUIDELINES

The authors Harold Pimentel, Zhiyue Hu and Haiyan Huang declare they have no conflict of interests.ƒ

This article does not contain any studies with human or animal subjects performed by any of the authors.

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