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]"          # XGBoostCCA, LightGBMCCA, CatBoostCCA
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 sklearn.model_selection import train_test_split

from cca_zoo.datasets import make_joint_data
from cca_zoo.linear import CCA

# Generate correlated two-view data from a linear latent variable model
views = make_joint_data(
    n_samples=400,
    n_features=[50, 50],
    n_components=2,
    signal_to_noise=2.0,
    random_state=0,
)
X1_train, X1_test, X2_train, X2_test = train_test_split(
    *views, test_size=0.5, random_state=0
)
train_views, test_views = [X1_train, X2_train], [X1_test, X2_test]

# Fit CCA and evaluate
model = CCA(n_components=2).fit(train_views)
print(model.score(test_views))  # mean canonical correlation

# 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	Citation	Views
CCA	Standard CCA	Hotelling (1936)	2
RidgeCCA	Regularised CCA / canonical ridge	Vinod (1976)	2
PLS	Partial Least Squares	Wold (1975)	2
MCCA	Multiset CCA — pairwise sum objective	Kettenring (1971)	≥2
GCCA	Generalised CCA — shared latent projection	Carroll (1968)	≥2
TCCA	Tensor CCA — higher-order cross-moment	Luo et al. (2015)	≥2
PartialCCA	CCA adjusted for confounding variables	Rao (1969)	≥2
GRCCA	Group-regularised CCA	Tuzhilina, Tozzi & Hastie (2023)	≥2
CCAR3	CCA via reduced-rank regression, row-sparse in high dimensions	Donnat & Tuzhilina (2024)	2
ECCA	CCA via reduced-rank regression, entrywise-sparse (ccar3 package's ecca)	Donnat & Tuzhilina (2024)	2
GraphicalLassoCCA	MCCA with an L1-penalised sparse-precision within-view covariance	Friedman, Hastie & Tibshirani (2008)	≥2
CCAEY	Eckart-Young CCA, full-batch L-BFGS-B (2 or more views)	Chapman, Wells & Lawry Aguila (2024)	≥2
PLSEY	Eckart-Young PLS, full-batch L-BFGS-B	Chapman, Wells & Lawry Aguila (2024)	≥2
HuberCCA	Bounded-influence (Huber-style) EY-CCA, robust to high-leverage outliers	Filzmoser, Dehon & Croux (2000)	≥2
RANSACCCA	Robust CCA via random sample consensus, robust to mismatched/corrupted rows	Chapman et al. (2021)	≥2
TrimmedCCA	Robust CCA via LTS/MCD-style concentration steps, holds up near ~50% contamination	Rousseeuw & Van Driessen (1999)	≥2
ProjectionPursuitCCA	Robust CCA by projection pursuit, maximising Spearman's rank correlation	Alfons, Croux & Filzmoser (2017)	≥2

cca_zoo.nonparametric

Class	Description	Citation
KCCA	Kernel CCA	Hardoon, Szedmak & Shawe-Taylor (2004)
KGCCA	Kernel Generalised CCA	Tenenhaus, Philippe & Frouin (2015)
KTCCA	Kernel Tensor CCA	Luo et al. (2015)
ManifoldCCA	Transductive CCA over a shared graph Laplacian or LLE operator	Belkin & Niyogi (2003); Roweis & Saul (2000)

cca_zoo.tree (requires [tree])

Class	Description	Citation	Views
XGBoostCCA	Gradient-boosted-tree CCA via XGBoost (Eckart-Young objective)	Chapman (2026)	≥2
LightGBMCCA	Gradient-boosted-tree CCA via LightGBM (Eckart-Young objective)	Chapman (2026)	≥2
CatBoostCCA	Gradient-boosted-tree CCA via CatBoost (Eckart-Young objective)	Chapman (2026)	≥2

cca_zoo.gam

Class	Description	Citation	Views
GAMCCA	Generalized-additive-model CCA (Eckart-Young objective)	Chapman et al. (2021)	≥2
MARSCCA	Multivariate-adaptive-regression-spline CCA with optional within-view interactions (Eckart-Young objective)	Chapman et al. (2021); Friedman (1991)	≥2

cca_zoo.gp

Class	Description	Citation	Views
GaussianProcessCCA	Gaussian-process CCA (Eckart-Young objective), with predictive uncertainty	Chapman et al. (2021)	≥2

cca_zoo.sparse

Class	Description	Citation	Views
ElasticNetCCA	Sparse linear CCA via coordinate descent (Eckart-Young objective)	Chapman et al. (2021)	≥2
MultiTaskElasticNetCCA	ElasticNetCCA with row-group sparsity shared across latent dimensions	Chapman et al. (2021)	≥2
OrthogonalMatchingPursuitCCA	Fixed-cardinality sparse linear CCA via greedy selection (Eckart-Young objective)	Chapman et al. (2021)	≥2
PMDCCA	Sparse CCA via PMD	Witten, Tibshirani & Hastie (2009)	≥2
ADMMCCA	Sparse CCA via ADMM	Suo et al. (2017)	≥2
IPLSCCA	Sparse CCA by alternating elastic-net regressions	Waaijenborg, de Witt Hamer & Zwinderman (2008); Mai & Zhang (2019)	≥2
SpanCCA	Hard-threshold ALS inspired by the SpanCCA algorithm	Asteris, Kyrillidis, Koyejo & Poldrack (2016)	≥2
ParkhomenkoCCA	Soft-threshold sparse CCA	Parkhomenko, Tritchler & Beyene (2009)	≥2
SAR	Sparse alternating regression, BIC-selected penalty	Wilms & Croux (2015)	≥2

cca_zoo.stochastic

Class	Description	Citation	Views
StochasticCCAEY	CCAEY, fit by mini-batch SGD	Chapman, Wells & Lawry Aguila (2024)	≥2

cca_zoo.deep (requires [deep])

Built on PyTorch Lightning — models are trained with a standard lightning.Trainer, not a fit() wrapper, and trainer.predict returns each view's encoding. See the deep learning guide.

Class	Description	Citation	Views
DCCA	Deep CCA	Andrew et al. (2013)	2
DMCCA	Deep multiset CCA, pairwise-sum objective	Somandepalli et al. (2019)	≥2
DPCCA	Deep partial CCA: correlation conditioned on a variable only needed for training	Rotman, Vulić & Reichart (2018)	≥2
DGCCA	Deep generalised CCA	Benton et al. (2019)	≥2
DTCCA	Deep tensor CCA	Wong et al. (2021)	≥2
DCCAEY	Deep CCA via Eigengame / Eckart-Young objective	Chapman, Wells & Lawry Aguila (2024)	≥2
DCCANOI	Deep CCA via non-linear orthogonal iterations	Wang et al. (2015)	≥2
DCCASDL	Deep CCA via stochastic decorrelation loss	Chang, Xiang & Hospedales (2018)	≥2
DCCAE	Deep CCA with autoencoder reconstruction	Wang et al. (2015)	≥2
DVCCA	Deep variational CCA	Wang et al. (2016)	≥2
DVCCAPrivate	Deep variational CCA with private latents per view	Wang et al. (2016)	≥2
SplitAE	Split autoencoder baseline	Wang et al. (2015)	≥2
BarlowTwins	Self-supervised learning via redundancy reduction	Zbontar et al. (2021)	≥2
VICReg	Variance-Invariance-Covariance Regularization	Bardes, Ponce & LeCun (2022)	≥2
NRDCCA	Deep CCA with noise regularisation against model collapse	He et al. (2024)	≥2
LeJEPA	Joint-embedding prediction with SIGReg against collapse	Balestriero & LeCun (2025)	≥2

Losses defined between two views (BarlowTwins, VICReg, DCCASDL, DCCAE's default) are summed over pairs of views, as DMCCA sums DCCA's; with two views each is the published loss.

cca_zoo.probabilistic

Class	Description	Citation
GFA	Group Factor Analysis, per-view ARD; no extra dependencies	Klami et al. (2015)
ProbabilisticCCA (requires [probabilistic])	MCMC via NumPyro	Bach & Jordan (2005)
VariationalBayesCCA (requires [probabilistic])	Variational inference + ARD via NumPyro	Wang (2007)

cca_zoo.model_selection

Class	Description	Citation
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. Please also read our Code of Conduct.

Found a security issue? See SECURITY.md for how to report it privately.