  Sparse canonical correlation analysis (CCA) is a useful statistical tool to
detect latent information with sparse structures. However, sparse CCA works
only for two datasets, i.e., there are only two views or two distinct objects.
To overcome this limitation, in this paper, we propose a sparse generalized
canonical correlation analysis (GCCA), which could detect the latent relations
of multiview data with sparse structures. Moreover, the introduced sparsity
could be considered as Laplace prior on the canonical variates. Specifically,
we convert the GCCA into a linear system of equations and impose $\ell_1$
minimization penalty for sparsity pursuit. This results in a nonconvex problem
on Stiefel manifold, which is difficult to solve. Motivated by Boyd's consensus
problem, an algorithm based on distributed alternating iteration approach is
developed and theoretical consistency analysis is investigated elaborately
under mild conditions. Experiments on several synthetic and real world datasets
demonstrate the effectiveness of the proposed algorithm.
