Nonlinear Sparse Generalized Canonical Correlation Analysis

Official Python implementation of NSGCCA, from the following paper:

Nonlinear Sparse Generalized Canonical Correlation Analysis for Multi-view High-dimensional Data.
Rong Wu, Ziqi Chen, Gen Li and Hai Shu.
New York University
[arXiv]

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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 variable selection.

Installation

Requirements: Python 3.10 Clone this repository and install other required packages:

git clone git@github.com:Rows21/NSGCCA
cd NSGCCA
conda env create -f env.yml

Model Training

Datasets

• Synthetic Datasets synth_data.py
• TCGA Breast Cancer Database in Realdata from (https://tcga-data.nci.nih.gov/docs/publications)

(Feel free to post suggestions in issues of recommending latest proposed CCA network for comparison. Currently, the baselines folder is to put comparable models.)

Hyper-parameter tuning

We design hyper-parameter tuning before function executions:

HSIC-SGCCA

Use function: solver.tune_hyper(views, k=5, mode='cv')

TS-KGCCA & SA-KGCCA

The hyper-paramter tuning structures are built-in functions.

Training

• Follow the Tutorial file for training HSIC-SGCCA, SA-KGCCA and TS-KGCCA.

## For HSIC-SGCCA
u = solver.SNGCCA.fit_admm(views, constraint=constraint)

## For TS-KGCCA
s_k, u = tskgcca(views)

## For SA-KGCCA
u = sakgcca(views)

• Note that for KGCCA component in TS-KGCCA, we use function tskcca_post in the tskgcca_post file for simulation and tskgcca_post_real file for real data example.
• Higher-stage calculation is controlled by stage = n.

Results

Simulation Studies

FIgure 1: The variable selection performance are processed through Select.Rmd.
Figure 2: The Normalized sample HSIC performance are calculated through CKA.Rmd.
Figure 3: The scatter plots are generated through Linear_Combination.Rmd.

Real-World Studies -- TCGA breast cancer database

Data_download_preprocess: TCGA-BRCA preprocessing through R script.
Venn Diagram: The clustering results for TCGA-BRCA. Survival model is processed through XGBoost-AFT model and SurvivalEVAL package.

Citation

If you find this repository helpful, please consider citing:

@article{wu2025nonlinear,
  title={Nonlinear Sparse Generalized Canonical Correlation Analysis for Multi-view High-dimensional Data},
  author={Wu, Rong and Chen, Ziqi and Li, Gen and Shu, Hai},
  journal={arXiv preprint arXiv:2502.18756},
  year={2025}
}

Acknowledgement

This repository is built using the timm library.

License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

© 2025 Rong Wu. You are free to share and adapt the material with attribution.