Nonlinear Sparse Generalized Canonical Correlation Analysis for Multi-view High-dimensional Data

TL;DR

This paper introduces three novel nonlinear sparse generalized CCA methods designed for multi-view high-dimensional data, effectively addressing the integration of nonlinearity, sparsity, and multiple data views.

Contribution

The paper develops three new methods extending existing CCA techniques to multi-view settings, incorporating nonlinearity and sparsity, and introduces a novel optimization approach for HSIC-SGCCA.

Findings

HSIC-SGCCA outperforms competing methods in variable selection.

The methods successfully handle multi-view high-dimensional datasets.

Efficient optimization algorithms are developed for nonconvex problems.

Abstract

Motivation: Biomedical studies increasingly produce multi-view high-dimensional datasets (e.g., multi-omics) that demand integrative analysis. Existing canonical correlation analysis (CCA) and generalized CCA methods address at most two of the following three key aspects simultaneously: (i) nonlinear dependence, (ii) sparsity for variable selection, and (iii) generalization to more than two data views. There is a pressing need for CCA methods that integrate all three aspects to effectively analyze multi-view high-dimensional data. Results: We propose three nonlinear, sparse, generalized CCA methods, HSIC-SGCCA, SA-KGCCA, and TS-KGCCA, for variable selection in multi-view high-dimensional data. These methods extend existing SCCA-HSIC, SA-KCCA, and TS-KCCA from two-view to multi-view settings. While SA-KGCCA and TS-KGCCA yield multi-convex optimization problems solved via block coordinate descent, HSIC-SGCCA introduces a necessary unit-variance constraint previously ignored in SCCA-HSIC, resulting in a nonconvex, non-multiconvex problem. We efficiently address this challenge by integrating the block prox-linear method with the linearized alternating direction method of multipliers. Simulations and TCGA-BRCA data analysis demonstrate that HSIC-SGCCA outperforms competing methods in multi-view variable selection.