Joint Linked Component Analysis for Multiview Data
This method addresses the challenge of analyzing multiview data more efficiently for researchers in fields like bioinformatics or computer vision, though it appears incremental as it builds on existing component analysis techniques.
The authors tackled the problem of extracting shared and individual components from multiview data by proposing joint linked component analysis, which simultaneously estimates view-specific loading matrices and the rank of the common latent subspace, resulting in a clean SVD representation for cross-covariance.
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.