  Multiview canonical correlation analysis (MCCA) seeks latent low-dimensional
representations encountered with multiview data of shared entities (a.k.a.
common sources). However, existing MCCA approaches do not exploit the geometry
of the common sources, which may be available \emph{a priori}, or can be
constructed using certain domain knowledge. This prior information about the
common sources can be encoded by a graph, and be invoked as a regularizer to
enrich the maximum variance MCCA framework. In this context, the present
paper's novel graph-regularized (G) MCCA approach minimizes the distance
between the wanted canonical variables and the common low-dimensional
representations, while accounting for graph-induced knowledge of the common
sources. Relying on a function capturing the extent low-dimensional
representations of the multiple views are similar, a generalization bound of
GMCCA is established based on Rademacher's complexity. Tailored for setups
where the number of data pairs is smaller than the data vector dimensions, a
graph-regularized dual MCCA approach is also developed. To further deal with
nonlinearities present in the data, graph-regularized kernel MCCA variants are
put forward too. Interestingly, solutions of the graph-regularized linear,
dual, and kernel MCCA, are all provided in terms of generalized eigenvalue
decomposition. Several corroborating numerical tests using real datasets are
provided to showcase the merits of the graph-regularized MCCA variants relative
to several competing alternatives including MCCA, Laplacian-regularized MCCA,
and (graph-regularized) PCA.
