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

arXiv: https://arxiv.org/abs/1611.01066 · HTML: https://mlsanity.com/paper/1611.01066/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2016.

## Built on by (most cited first, 7 of 7)

- [Deep IDA: A Deep Learning Method for Integrative Discriminant Analysis of Multi-View Data with Feature Ranking -- An Application to COVID-19 severity](https://mlsanity.com/paper/2111.09964/) (2021)
- [Interpretable Deep Learning Methods for Multiview Learning](https://mlsanity.com/paper/2302.07930/) (2023)
- [Generalized Eigenvalue Problems with Generative Priors](https://mlsanity.com/paper/2411.01326/) (2024)
- [Scalable Randomized Kernel Methods for Multiview Data Integration and Prediction](https://mlsanity.com/paper/2304.04692/) (2023)
- [Extensions of Heterogeneity in Integration and Prediction (HIP) with R Shiny Application](https://mlsanity.com/paper/2310.08426/) (2023)
- [mvlearnR and Shiny App for multiview learning](https://mlsanity.com/paper/2311.16181/) (2023)
- [A deep learning pipeline for cross-sectional and longitudinal multiview data integration](https://mlsanity.com/paper/2312.01238/) (2023)

## Abstract (arXiv)

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.