Graph Canonical Correlation Analysis

TL;DR

This paper introduces graph Canonical Correlation Analysis (gCCA), a novel method that leverages graph structures to improve correlation estimation between two multivariate datasets, with theoretical guarantees and superior performance demonstrated through simulations and real multiomics data.

Contribution

The paper proposes gCCA, a new structured CCA method incorporating graph information, along with efficient algorithms and theoretical analysis for finite sample performance.

Findings

gCCA outperforms existing CCA methods in simulations

gCCA successfully identifies gene regulation pathways in multiomics data

Theoretical results provide finite sample guarantees for gCCA

Abstract

Canonical correlation analysis (CCA) is a widely used technique for estimating associations between two sets of multi-dimensional variables. Recent advancements in CCA methods have expanded their application to decipher the interactions of multiomics datasets, imaging-omics datasets, and more. However, conventional CCA methods are limited in their ability to incorporate structured patterns in the cross-correlation matrix, potentially leading to suboptimal estimations. To address this limitation, we propose the graph Canonical Correlation Analysis (gCCA) approach, which calculates canonical correlations based on the graph structure of the cross-correlation matrix between the two sets of variables. We develop computationally efficient algorithms for gCCA, and provide theoretical results for finite sample analysis of best subset selection and canonical correlation estimation by introducing concentration inequalities and stopping time rule based on martingale theories. Extensive simulations demonstrate that gCCA outperforms competing CCA methods. Additionally, we apply gCCA to a multiomics dataset of DNA methylation and RNA-seq transcriptomics, identifying both positively and negatively regulated gene expression pathways by DNA methylation pathways.