  In this work, we propose the joint linked component analysis (joint\_LCA) for
multiview data. Unlike classic methods which extract the shared components in a
sequential manner, the objective of joint\_LCA is to identify the view-specific
loading matrices and the rank of the common latent subspace simultaneously. We
formulate a matrix decomposition model where a joint structure and an
individual structure are present in each data view, which enables us to arrive
at a clean svd representation for the cross covariance between any pair of data
views. An objective function with a novel penalty term is then proposed to
achieve simultaneous estimation and rank selection. In addition, a refitting
procedure is employed as a remedy to reduce the shrinkage bias caused by the
penalization.
