  Integration of multi-omics data provides opportunities for revealing
biological mechanisms related to certain phenotypes. We propose a novel method
of multi-omics integration called supervised deep generalized canonical
correlation analysis (SDGCCA) for modeling correlation structures between
nonlinear multi-omics manifolds, aiming for improving classification of
phenotypes and revealing biomarkers related to phenotypes. SDGCCA addresses the
limitations of other canonical correlation analysis (CCA)-based models (e.g.,
deep CCA, deep generalized CCA) by considering complex/nonlinear cross-data
correlations and discriminating phenotype groups. Although there are a few
methods for nonlinear CCA projections for discriminant purposes of phenotypes,
they only consider two views. On the other hand, SDGCCA is the nonlinear
multiview CCA projection method for discrimination. When we applied SDGCCA to
prediction of patients of Alzheimer's disease (AD) and discrimination of early-
and late-stage cancers, it outperformed other CCA-based methods and other
supervised methods. In addition, we demonstrate that SDGCCA can be used for
feature selection to identify important multi-omics biomarkers. In the
application on AD data, SDGCCA identified clusters of genes in multi-omics
data, which are well known to be associated with AD.
