Sparse Generalized Eigenvalue Problem with Application to Canonical Correlation Analysis for Integrative Analysis of Methylation and Gene Expression Data

TL;DR

This paper introduces SELP, a sparse estimation framework for generalized eigenvalue problems, applied to canonical correlation analysis of methylation and gene expression data, revealing biologically relevant insights.

Contribution

The paper proposes a novel sparse estimation method called SELP for generalized eigenvalue problems, enhancing integrative analysis of high-dimensional biological data.

Findings

SELP effectively identifies meaningful biological signals.

The method performs competitively in simulations.

Application reveals genes linked to breast cancer.

Abstract

We present a method for individual and integrative analysis of high dimension, low sample size data that capitalizes on the recurring theme in multivariate analysis of projecting higher dimensional data onto a few meaningful directions that are solutions to a generalized eigenvalue problem. We propose a general framework, called SELP (Sparse Estimation with Linear Programming), with which one can obtain a sparse estimate for a solution vector of a generalized eigenvalue problem. We demonstrate the utility of SELP on canonical correlation analysis for an integrative analysis of methylation and gene expression profiles from a breast cancer study, and we identify some genes known to be associated with breast carcinogenesis, which indicates that the proposed method is capable of generating biologically meaningful insights. Simulation studies suggest that the proposed method performs competitive in comparison with some existing methods in identifying true signals in various underlying covariance structures.