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Sparse Canonical Covariance Analysis for High-throughput Data

Author

Listed:
  • Lee Woojoo

    (Karolinska Institutet)

  • Lee Donghwan

    (Seoul National University)

  • Lee Youngjo

    (Seoul National University)

  • Pawitan Yudi

    (Karolinska Institutet)

Abstract

Canonical covariance analysis (CCA) has gained popularity as a method for the analysis of two sets of high-dimensional genomic data. However, it is often difficult to interpret the results because canonical vectors are linear combinations of all variables, and the coefficients are typically nonzero. Several sparse CCA methods have recently been proposed for reducing the number of nonzero coefficients, but these existing methods are not satisfactory because they still give too many nonzero coefficients. In this paper, we propose a new random-effect model approach for sparse CCA; the proposed algorithm can adapt arbitrary penalty functions to CCA without much computational demands. Through simulation studies, we compare various penalty functions in terms of the performance of correct model identification. We also develop an extension of sparse CCA to address more than two sets of variables on the same set of observations. We illustrate the method with an analysis of the NCI cancer dataset.

Suggested Citation

  • Lee Woojoo & Lee Donghwan & Lee Youngjo & Pawitan Yudi, 2011. "Sparse Canonical Covariance Analysis for High-throughput Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-24, July.
    • Handle: RePEc:bpj:sagmbi:v:10:y:2011:i:1:n:30
    DOI: 10.2202/1544-6115.1638
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    References listed on IDEAS

    as
    1. Johnstone, Iain M. & Lu, Arthur Yu, 2009. "On Consistency and Sparsity for Principal Components Analysis in High Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 682-693.
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    3. A. Salim & Y. Pawitan & K. Bond, 2005. "Modelling association between two irregularly observed spatiotemporal processes by using maximum covariance analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 555-573, June.
    4. Hyonho Chun & Sündüz Keleş, 2010. "Sparse partial least squares regression for simultaneous dimension reduction and variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 3-25, January.
    5. Witten Daniela M & Tibshirani Robert J., 2009. "Extensions of Sparse Canonical Correlation Analysis with Applications to Genomic Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-27, June.
    6. Rothman, Adam J. & Levina, Elizaveta & Zhu, Ji, 2009. "Generalized Thresholding of Large Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 177-186.
    7. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
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    Cited by:

    1. Wang, Wenjia & Zhou, Yi-Hui, 2021. "Eigenvector-based sparse canonical correlation analysis: Fast computation for estimation of multiple canonical vectors," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    2. Kwon, Sunghoon & Oh, Seungyoung & Lee, Youngjo, 2016. "The use of random-effect models for high-dimensional variable selection problems," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 401-412.
    3. Lee, Youngjo & Oh, Hee-Seok, 2014. "A new sparse variable selection via random-effect model," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 89-99.

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