Sparse and Integrative Principal Component Analysis for Multiview Data

TL;DR

This paper introduces a novel sparse PCA method for multiview data that enforces elementwise and block sparsity, utilizing a Fantope-based optimization and ADMM algorithm, with proven convergence and support recovery.

Contribution

It develops a new multiview sparse PCA framework with a Fantope-based penalty and provides theoretical guarantees for convergence and sparsity recovery.

Findings

Method effectively recovers sparse eigenvectors in multiview data.

Theoretical convergence and support recovery are established.

Numerical studies demonstrate the method's practical performance.

Abstract

We consider dimension reduction of multiview data, which are emerging in scientific studies. Formulating multiview data as multi-variate data with block structures corresponding to the different views, or views of data, we estimate top eigenvectors from multiview data that have two-fold sparsity, elementwise sparsity and blockwise sparsity. We propose a Fantope-based optimization criterion with multiple penalties to enforce the desired sparsity patterns and a denoising step is employed to handle potential presence of heteroskedastic noise across different data views. An alternating direction method of multipliers (ADMM) algorithm is used for optimization. We derive the l2 convergence of the estimated top eigenvectors and establish their sparsity and support recovery properties. Numerical studies are used to illustrate the proposed method.