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Canonical correlation analysis (CCA) is a standard tool for studyingassociations between two data sources; however, it is not designed for datawith count or proportion measurement types. In addition, while CCA uncoverscommon signals, it does not elucidate which signals are unique to each datasource. To address these challenges, we propose a new framework for CCA basedon exponential families with explicit modeling of both common andsource-specific signals. Unlike previous methods based on exponential families,the common signals from our model coincide with canonical variables in GaussianCCA, and the unique signals are exactly orthogonal. These modeling differenceslead to a non-trivial estimation via optimization with orthogonalityconstraints, for which we develop an iterative algorithm based on a splittingmethod. Simulations show on par or superior performance of the proposed methodcompared to the available alternatives. We apply the method to analyzeassociations between gene expressions and lipids concentrations in nutrigenomicstudy, and to analyze associations between two distinct cell-type deconvolutionmethods in prostate cancer tumor heterogeneity study.

Exponential canonical correlation analysis with orthogonal variation