Extensions of Sparse Canonical Correlation Analysis with Applications to Genomic Data

Abstract

In recent work, several authors have introduced methods for sparse canonical correlation analysis (sparse CCA). Suppose that two sets of measurements are available on the same set of observations. Sparse CCA is a method for identifying sparse linear combinations of the two sets of variables that are highly correlated with each other. It has been shown to be useful in the analysis of high-dimensional genomic data, when two sets of assays are available on the same set of samples. In this paper, we propose two extensions to the sparse CCA methodology. (1) Sparse CCA is an unsupervised method; that is, it does not make use of outcome measurements that may be available for each observation (e.g., survival time or cancer subtype). We propose an extension to sparse CCA, which we call sparse supervised CCA, which results in the identification of linear combinations of the two sets of variables that are correlated with each other and associated with the outcome. (2) It is becoming increasingly common for researchers to collect data on more than two assays on the same set of samples; for instance, SNP, gene expression, and DNA copy number measurements may all be available. We develop sparse multiple CCA in order to extend the sparse CCA methodology to the case of more than two data sets. We demonstrate these new methods on simulated data and on a recently published and publicly available diffuse large B-cell lymphoma data set.

Auxiliary Training Information Assisted Visual Recognition

“…As an extended version of gCCA, it iteratively optimizes each onedimensional projection vectors (one column of W j ), and all d columns of W j are pursued one by one, similar to the algorithm presented in Ref. [38].…”

“…The classical Canonical Correlation Analysis (CCA) (see Refs. [13], [14], [38]) and its variants have been popular among practitioners for decades. In its basic form, the CCA algorithm finds a pair of linear projection vectors that maximize the linear correlation:…”

Joint sparse canonical correlation analysis for detecting differential imaging genetics modules

“…By imposing sparse regularization on the canonical vectors, sparse CCA can achieve better model fitting with variable selection. In this paper, we adopt the formulation in (Witten and Tibshirani, 2009) with L 1 regularization as follows:…”

“…In (2), the variance matrix of X and Y is treated as diagonal matrix, which has shown to be effective and efficient for high-dimensional data (Grellmann et al, 2015;Witten and Tibshirani, 2009). …”

“…To address this problem, penalized CCA and related methods were introduced by employing sparse penalties to select a small number of features. Examples include sparse CCA (Parkhomenko et al, 2009;Witten and Tibshirani, 2009), sparse PLS (Chun and Keles¸, 2010) and sparse reduced rank regression (Vounou et al, 2010), which have been demonstrated to be effective in detecting multivariate genomic and brain imaging associations (Grellmann et al, 2015;Liu and Calhoun, 2014). To incorporate biological prior knowledge and data structures to guide the search of associations, group SCCA (Lin et al, 2014) and network-guided sparse reduced rank regression (Wang et al, 2014) were proposed, which can further improve variable selection.…”