Robust Sparse Canonical Correlation Analysis

Abstract

Background: Canonical correlation analysis (CCA) is a multivariate statistical method which describes the associations between two sets of variables. The objective is to find linear combinations of the variables in each data set having maximal correlation. In genomics, CCA has become increasingly important to estimate the associations between gene expression data and DNA copy number change data. The identification of such associations might help to increase our understanding of the development of diseases such as cancer. However, these data sets are typically high-dimensional, containing a lot of variables relative to the number of objects. Moreover, the data sets might contain atypical observations since it is likely that objects react differently to treatments. We discuss a method for Robust Sparse CCA, thereby providing a solution to both issues. Sparse estimation produces canonical vectors with some of their elements estimated as exactly zero. As such, their interpretability is improved. Robust methods can cope with atypical observations in the data. Results: We illustrate the good performance of the Robust Sparse CCA method by several simulation studies and three biometric examples. Robust Sparse CCA considerably outperforms its main alternatives in (1) correctly detecting the main associations between the data sets, in (2) accurately estimating these associations, and in (3) detecting outliers. Conclusions: Robust Sparse CCA delivers interpretable canonical vectors, while at the same time coping with outlying observations. The proposed method is able to describe the associations between high-dimensional data sets, which are nowadays commonplace in genomics. Furthermore, the Robust Sparse CCA method allows to characterize outliers.

Multi-region brain transcriptomes uncover two subtypes of aging individuals with differences in Alzheimer risk and the impact ofAPOEε4

“…S5A). We considered a maximum of 𝑐𝑐𝑟𝑟𝑟𝑟𝑟𝑟 =10 canonical variates as in other high-dimensional data (38). We extract first 𝑘𝑘 canonical variates that maximize the ratio 𝜑𝜑 � 𝑗𝑗 = 𝜌𝜌 � 𝑗𝑗 /𝜌𝜌 � 𝑗𝑗+1 over the set of 𝑗𝑗 = 1, … , 𝑐𝑐𝑟𝑟𝑟𝑟𝑟𝑟 − 1.…”

Reference trait analysis reveals correlations between gene expression and quantitative traits in disjoint samples

“…For datasets with a very large number of reference and/or target traits (i.e. p ≫ n ), sparse canonical correlation analysis (Witten and Tibshirani 2009; Wilms and Croux 2016) may reduce over-fitting, but this situation is not common when relating two sets of traits U and V that contain organism-level phenotypes as opposed to molecular features.…”

“…We anticipate that the framework outlined in this study will be increasingly useful as studies of diverse, genetically unique populations become more widespread. A useful future extension to this approach would incorporate statistical techniques such as sparse canonical correlation analysis (Witten and Tibshirani 2009; Wilms and Croux 2016), which could permit inference in phenome-level studies where the target or reference traits are high dimensional. Overall, our approach is likely to be particularly important in functional genomics studies, those utilizing post-mortem subjects, and large population studies in which individuals are unavailable for further characterization.…”

A data‐driven investigation of relationships between bipolar psychotic symptoms and schizophrenia genome‐wide significant genetic loci

“…The techniques introduced by Waaijenborg, Verselewel de Witt Hamer, and Zwinderman (), Parkhomenko, Tritchler, and Beyene (), and Witten et al () impose covariance restrictions. Wilms et al () suggested that variables are selected (find a sparse solution) using a penalized regression framework. Wilms et al () demonstrated that this method outperforms CCA and some other sparse CCA approaches in almost all simulated scenarios.…”

“…Wilms et al () suggested that variables are selected (find a sparse solution) using a penalized regression framework. Wilms et al () demonstrated that this method outperforms CCA and some other sparse CCA approaches in almost all simulated scenarios. This methodology is freely available in package “PMA” in R on CRAN, and we chose to use it for the analyses in this study.…”