Eigenvector-based sparse canonical correlation analysis: Fast computation for estimation of multiple canonical vectors
提出一种基于特征向量的稀疏典型相关分析算法，可同时估计多个典型对，支持并行计算，在GTEx甲状腺组织图像、SNP与RNA-seq基因表达、微生物组等数据中表现优于传统方法。
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.