# Sparse and Integrative Principal Component Analysis for Multiview Data

arXiv: https://arxiv.org/abs/2301.06718 · HTML: https://mlsanity.com/paper/2301.06718/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2023.

## Built on by (most cited first, 2 of 2)

- [A spectral method for multi-view subspace learning using the product of projections](https://mlsanity.com/paper/2410.19125/) (2024)
- [Representation Retrieval Learning for Heterogeneous Data Integration](https://mlsanity.com/paper/2503.09494/) (2025)

## Abstract (arXiv)

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.