Joint Linked Component Analysis for Multiview Data
Lin Xiao, Luo Xiao
TL;DR
The paper introduces joint_LCA, a method for multiview data that jointly estimates the rank of the shared latent subspace and the view-specific loading matrices, while decomposing each view into joint and individual components. It forms a penalized optimization on cross-covariances with a group-sparsity penalty to select the common rank and uses an alternating Procrustes-based algorithm plus a per-component refinement, including a model refitting step to reduce shrinkage bias. Through extensive simulations and real-data applications across biological and socio-economic domains, it demonstrates robust rank identification, accurate loading estimation, and interpretable common components, often outperforming sequential CCA-based approaches and JIVE. The method is adaptable to multiple views and sets the stage for future high-dimensional extensions with sparsity constraints and scalable computation. Overall, joint_LCA provides a principled, data-driven approach to uncover and quantify shared structure across diverse data sources, with practical implications for integrative analyses.
Abstract
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.