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Eigenvector-based sparse canonical correlation analysis: fast computation for estimation of multiple canonical vectors. (English) Zbl 1476.62117

Summary: Classical canonical correlation analysis (CCA) requires matrices to be low dimensional, i.e. the number of features cannot exceed the sample size. Recent developments in CCA have mainly focused on the high-dimensional setting, where the number of features in both matrices under analysis greatly exceeds the sample size. These approaches impose penalties in the optimization problems that are needed to be solve iteratively, and estimate multiple canonical vectors sequentially. In this work, we provide an explicit link between sparse multiple regression with sparse canonical correlation analysis, and an efficient algorithm that can estimate multiple canonical pairs simultaneously rather than sequentially. Furthermore, the algorithm naturally allows parallel computing. These properties make the algorithm much efficient. We provide theoretical results on the consistency of canonical pairs. The algorithm and theoretical development are based on solving an eigenvectors problem, which significantly differentiate our method with existing methods. Simulation results support the improved performance of the proposed approach. We apply eigenvector-based CCA to analysis of the GTEx thyroid histology images, analysis of SNPs and RNA-seq gene expression data, and a microbiome study. The real data analysis also shows improved performance compared to traditional sparse CCA.

MSC:

62H20 Measures of association (correlation, canonical correlation, etc.)
62H12 Estimation in multivariate analysis
62J07 Ridge regression; shrinkage estimators (Lasso)
62P10 Applications of statistics to biology and medical sciences; meta analysis
92D20 Protein sequences, DNA sequences

Software:

RGCCA; scca; PMA; glmnet; CCA; Ebimage; GPLP
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References:

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