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

arXiv: https://arxiv.org/abs/2502.18756 · HTML: https://mlsanity.com/paper/2502.18756/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 73 references that are in the map.
- First posted on arXiv 26 Feb 2025.

## Builds on (most cited first, 15 of 15)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [On Deep Multi-View Representation Learning: Objectives and Optimization](https://mlsanity.com/paper/1602.01024/) (2016)
- [Neuron Shapley: Discovering the Responsible Neurons](https://mlsanity.com/paper/2002.09815/) (2020)
- [Survival regression with accelerated failure time model in XGBoost](https://mlsanity.com/paper/2006.04920/) (2020)
- [Deep Generalized Canonical Correlation Analysis](https://mlsanity.com/paper/1702.02519/) (2017)
- [A globally convergent algorithm for nonconvex optimization based on block coordinate update](https://mlsanity.com/paper/1410.1386/) (2014)
- [Statistical and computational trade-offs in estimation of sparse principal components](https://mlsanity.com/paper/1408.5369/) (2014)
- [Sparse CCA: Adaptive Estimation and Computational Barriers](https://mlsanity.com/paper/1409.8565/) (2014)
- [Adaptivity and Computation-Statistics Tradeoffs for Kernel and Distance based High Dimensional Two Sample Testing](https://mlsanity.com/paper/1508.00655/) (2015)
- [A convex formulation for high-dimensional sparse sliced inverse regression](https://mlsanity.com/paper/1809.06024/) (2018)
- [Structured SUMCOR Multiview Canonical Correlation Analysis for Large-Scale Data](https://mlsanity.com/paper/1804.08806/) (2018)
- [Scalable and Flexible Multiview MAX-VAR Canonical Correlation Analysis](https://mlsanity.com/paper/1605.09459/) (2016)
- [Sparse Generalized Canonical Correlation Analysis: Distributed Alternating Iteration based Approach](https://mlsanity.com/paper/2004.10981/) (2020)
- [High-Dimensional Sparse Single-Index Regression Via Hilbert-Schmidt Independence Criterion](https://mlsanity.com/paper/2105.08230/) (2021)

## Built on by (most cited first, 1 of 1)

- [Unpaired Canonical Correlation Analysis](https://mlsanity.com/paper/2610.09530/) (2026)

## Abstract (arXiv)

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.