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Modern biomedical studies often collect multi-view data, that is, multipletypes of data measured on the same set of objects. A popular model inhigh-dimensional multi-view data analysis is to decompose each view's datamatrix into a low-rank common-source matrix generated by latent factors commonacross all data views, a low-rank distinctive-source matrix corresponding toeach view, and an additive noise matrix. We propose a novel decompositionmethod for this model, called decomposition-based generalized canonicalcorrelation analysis (D-GCCA). The D-GCCA rigorously defines the decompositionon the L2 space of random variables in contrast to the Euclidean dot productspace used by most existing methods, thereby being able to provide theestimation consistency for the low-rank matrix recovery. Moreover, to wellcalibrate common latent factors, we impose a desirable orthogonality constrainton distinctive latent factors. Existing methods, however, inadequately considersuch orthogonality and may thus suffer from substantial loss of undetectedcommon-source variation. Our D-GCCA takes one step further than generalizedcanonical correlation analysis by separating common and distinctive componentsamong canonical variables, while enjoying an appealing interpretation from theperspective of principal component analysis. Furthermore, we propose to use thevariable-level proportion of signal variance explained by common or distinctivelatent factors for selecting the variables most influenced. Consistentestimators of our D-GCCA method are established with good finite-samplenumerical performance, and have closed-form expressions leading to efficientcomputation especially for large-scale data. The superiority of D-GCCA overstate-of-the-art methods is also corroborated in simulations and real-worlddata examples.

D-GCCA: Decomposition-based Generalized Canonical Correlation Analysis for Multi-view High-dimensional Data