Double-matched matrix decomposition for multi-view data

TL;DR

This paper introduces a novel double-matched matrix decomposition method for multi-view data, leveraging both sample and feature matching to improve extraction of joint and individual signals, demonstrated on biological and sports data.

Contribution

It proposes a new optimization-based approach for double-matched multi-view data decomposition, enhancing signal estimation by exploiting dual matching information.

Findings

Double-matched decomposition outperforms single-matching methods in simulations.

The method successfully identifies meaningful joint and individual signals in real datasets.

Application to miRNA and soccer data reveals domain-relevant insights.

Abstract

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.