# Double-matched matrix decomposition for multi-view data

arXiv: https://arxiv.org/abs/2105.03396 · HTML: https://mlsanity.com/paper/2105.03396/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 43 references that are in the map.
- First posted on arXiv 7 May 2021.

## Builds on (most cited first, 7 of 7)

- [Angle-Based Joint and Individual Variation Explained](https://mlsanity.com/paper/1704.02060/) (2017)
- [Structural Learning and Integrative Decomposition of Multi-View Data](https://mlsanity.com/paper/1707.06573/) (2017)
- [Linked Component Analysis from Matrices to High Order Tensors: Applications to Biomedical Data](https://mlsanity.com/paper/1508.07416/) (2015)
- [Integrative Factorization of Bidimensionally Linked Matrices](https://mlsanity.com/paper/1906.03722/) (2019)
- [Penalized Orthogonal Iteration for Sparse Estimation of Generalized Eigenvalue Problem](https://mlsanity.com/paper/1711.03170/) (2017)
- [Simultaneous Non-Gaussian Component Analysis (SING) for Data Integration in Neuroimaging](https://mlsanity.com/paper/2005.00597/) (2020)
- [Linked Matrix Factorization](https://mlsanity.com/paper/1710.02931/) (2017)

## Built on by (most cited first, 1 of 1)

- [Learning Joint and Individual Structure in Network Data with Covariates](https://mlsanity.com/paper/2406.08776/) (2024)

## Abstract (arXiv)

We consider the problem of extracting joint and individual signals from multi-view data, that is data collected from different sources on matched samples. While existing methods for multi-view data decomposition explore single matching of data by samples, we focus on double-matched multi-view data (matched by both samples and source features). Our motivating example is the miRNA data collected from both primary tumor and normal tissues of the same subjects; the measurements from two tissues are thus matched both by subjects and by miRNAs. Our proposed double-matched matrix decomposition allows to simultaneously extract joint and individual signals across subjects, as well as joint and individual signals across miRNAs. Our estimation approach takes advantage of double-matching by formulating a new type of optimization problem with explicit row space and column space constraints, for which we develop an efficient iterative algorithm. Numerical studies indicate that taking advantage of double-matching leads to superior signal estimation performance compared to existing multi-view data decomposition based on single-matching. We apply our method to miRNA data as well as data from the English Premier League soccer matches, and find joint and individual multi-view signals that align with domain specific knowledge.