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Canonical correlation analysis (CCA) is a classical and importantmultivariate technique for exploring the relationship between two sets ofcontinuous variables. CCA has applications in many fields, such as genomics andneuroimaging. It can extract meaningful features as well as use these featuresfor subsequent analysis. Although some sparse CCA methods have been developedto deal with high-dimensional problems, they are designed specifically forcontinuous data and do not consider the integer-valued data fromnext-generation sequencing platforms that exhibit very low counts for someimportant features. We propose a model-based probabilistic approach forcorrelation and canonical correlation estimation for two sparse count data sets(PSCCA). PSCCA demonstrates that correlations and canonical correlationsestimated at the natural parameter level are more appropriate than traditionalestimation methods applied to the raw data. We demonstrate through simulationstudies that PSCCA outperforms other standard correlation approaches and sparseCCA approaches in estimating the true correlations and canonical correlationsat the natural parameter level. We further apply the PSCCA method to study theassociation of miRNA and mRNA expression data sets from a squamous cell lungcancer study, finding that PSCCA can uncover a large number of stronglycorrelated pairs than standard correlation and other sparse CCA approaches.

Probabilistic Canonical Correlation Analysis for Sparse Count Data