CCA-Zoo

Multiview Canonical Correlation Analysis in Python

CCA-Zoo is a Python library of reference implementations of Canonical Correlation Analysis (CCA) algorithms from the literature, from classical CCA (Hotelling 1936) through sparse, kernel, deep, and probabilistic variants — each documented with the paper it comes from. It's also built to be used directly: every model follows the same scikit-learn estimator API (fit, transform, fit_transform, score), is fully typed (PEP 561), and is tested against known closed-form solutions where one exists.

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Installation

uv add cca-zoo        # or: pip install cca-zoo

Install optional extras as needed:

uv add "cca-zoo[deep]"          # DCCA variants (requires PyTorch + Lightning)
uv add "cca-zoo[probabilistic]" # Probabilistic CCA (requires NumPyro + JAX)
uv add "cca-zoo[tree]"          # TreeCCA (requires XGBoost, optionally LightGBM)
uv add "cca-zoo[all]"           # Everything above

(substitute pip install for uv add if you're not using uv)

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Quick start

from cca_zoo.datasets import JointData
from cca_zoo.linear import CCA

# Generate correlated two-view data from a linear latent variable model
data = JointData(
    n_views=2,
    n_samples=200,
    n_features=[50, 50],
    latent_dimensions=2,
    signal_to_noise=2.0,
    random_state=0,
)
train_views = data.sample()
test_views = data.sample()

# Fit CCA and evaluate
model = CCA(latent_dimensions=2).fit(train_views)
print(model.score(test_views))  # canonical correlations, shape (2,)

# Project views into the shared latent space
z1, z2 = model.transform(test_views)  # each shape (200, 2)

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Available methods

cca_zoo.linear

Class	Description	Views
CCA	Standard CCA (Hotelling 1936)	2
rCCA	Regularised CCA / canonical ridge	2
PLS	Partial Least Squares	2
MCCA	Multiset CCA — pairwise sum objective	≥2
GCCA	Generalised CCA — shared latent projection	≥2
TCCA	Tensor CCA — higher-order cross-moment	≥2
PartialCCA	CCA adjusted for confounding variables (Rao 1969)	≥2
GRCCA	Group-regularised CCA (Tuzhilina, Tozzi & Hastie 2021)	≥2
CCAR3	CCA via reduced-rank regression, row-sparse in high dimensions (Donnat & Tuzhilina 2024)	2
CCA_EY	Stochastic Eckart-Young CCA (unconstrained gradient descent)	2
PLS_EY	Stochastic Eckart-Young PLS (unconstrained gradient descent)	2
MCCA_EY	Multiview Eckart-Young CCA (unconstrained gradient descent)	≥2
SCCA_PMD	Sparse CCA via PMD (Witten 2009)	≥2
SCCA_ADMM	Sparse CCA via ADMM (Suo 2017)	≥2
SCCA_IPLS	Sparse CCA via iterative PLS (Mai & Zhang 2019)	≥2
SCCA_Span	Hard-threshold ALS inspired by SpanCCA (Asteris 2016)	≥2
ElasticCCA	Elastic net regularised CCA (Waaijenborg 2008)	≥2
ParkhomenkoCCA	Soft-threshold sparse CCA (Parkhomenko 2009)	≥2
SAR	Sparse alternating regression, BIC-selected penalty (Wilms & Croux 2015)	≥2
PLS_ALS	ALS variant of PLS (power iteration)	≥2

cca_zoo.nonparametric

Class	Description
KCCA	Kernel CCA
KGCCA	Kernel Generalised CCA
KTCCA	Kernel Tensor CCA

cca_zoo.tree (requires [tree])

Class	Description	Views
TreeCCA	Gradient-boosted-tree CCA (Eckart-Young objective)	≥2

cca_zoo.deep (requires [deep])

Built on PyTorch Lightning — models are trained with a standard lightning.Trainer, not a fit() wrapper. See the deep learning guide.

Class	Reference
DCCA	Andrew et al. 2013 — pluggable objective
DCCA_EY	Eigengame / Eckart-Young objective
DCCA_NOI	Wang et al. 2015 — non-linear orthogonal iterations
DCCA_SDL	Chang et al. 2018 — stochastic decorrelation loss
DCCAE	Wang et al. 2015 — with autoencoder reconstruction
DVCCA	Wang et al. 2016 — variational
DTCCA	Wong et al. 2021 — deep tensor CCA
DMCCA	Deep multiset CCA — pairwise-sum objective, ≥2 views
DGCCA	Benton et al. 2019 — deep generalised CCA, ≥2 views
SplitAE	Split autoencoder baseline
BarlowTwins	Zbontar et al. 2021
VICReg	Bardes et al. 2022

cca_zoo.probabilistic

Class	Reference
GFA	Klami, Virtanen & Kaski 2013 — Group Factor Analysis, per-view ARD; no extra dependencies
ProbabilisticCCA (requires [probabilistic])	Bach & Jordan 2005 — MCMC via NumPyro
VariationalBayesCCA (requires [probabilistic])	Wang 2007 — variational inference + ARD via NumPyro

cca_zoo.model_selection

Class	Description
GridSearchCV	Cross-validated hyperparameter search for multiview models

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Documentation

Full documentation, user guides, and API reference at: https://jameschapman19.github.io/cca_zoo/

See CHANGELOG.md for what's changed between releases.

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Citing

If CCA-Zoo is useful in your research, please cite:

@article{Chapman2021,
  title   = {{CCA-Zoo}: A collection of Regularized, Deep Learning based, Kernel,
             and Probabilistic {CCA} methods in a scikit-learn style framework},
  author  = {Chapman, James and Wang, Hao-Ting and Wells, Lennie and Wiesner, Johannes},
  journal = {Journal of Open Source Software},
  volume  = {6},
  number  = {68},
  pages   = {3823},
  year    = {2021},
  doi     = {10.21105/joss.03823},
}

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Contributing

Contributions are welcome. See docs/contributing.md for development setup, coding standards, and pull request guidelines.