Joint Linked Component Analysis for Multiview Data

TL;DR

This paper introduces joint linked component analysis (joint_LCA), a novel method for multiview data that simultaneously identifies view-specific and shared structures, improving upon sequential extraction approaches.

Contribution

The paper proposes a joint LCA model with a new penalty-based estimation and rank selection method, enabling simultaneous extraction of shared and view-specific components.

Findings

Effective in identifying shared and view-specific structures

Reduces bias through a refitting procedure

Provides a clear SVD-based representation for cross-covariance

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.