Multiset Canonical Correlation Analysis

Python implementation of multiset Canonical Correlation Analysis (mCCA) methods: sumcor, maxvar, minvar, ssqcor, genvar.

• Source-code: https://github.com/SSTGroup/multiset_canonical_correlation_analysis

Installing multiset_canonical_correlation_analysis

The only pre-requisite is to have Python 3 (>= version 3.11) installed. The mCCA package can be installed with

pip install multiset_canonical_correlation_analysis

Required third party packages will automatically be installed.

Quickstart

First, the imports:

import numpy as np
from multiset_canonical_correlation_analysis import mcca, simulations
from independent_vector_analysis.helpers_iva import _bss_isi

Create $K=100$ datasets with $T=10000$ samples of $N=5$ source components in each dataset. The $N$ SCVs all have a different maximum eigenvalue.

N = 5
K = 100
T = 10000
alpha = 1 - (K - np.array([10, 15, 20, 25, 30])) / (K - 1)
scv_cov = simulations.scv_covs_with_rank_R(N, K, 1, alpha=alpha, beta=0.0)
X, A, S = simulations.generate_datasets_from_covariance_matrices(scv_cov, T)

where

• S : true sources of dimensions N x T x K
• A : mixing matrix of dimensions N x N x K
• X : observed datasets of dimensions N x T x K

Apply mCCA-genvar to find the canonical variables.

transform, U = mcca.mcca(X, 'genvar')

where

• transform : transformation matrix of dimensions N x N x K
• U : canonical variables of dimensions N x T x K, with U[:,:,k] = transform[:,:,k].T @ X[:,:,k]

Calculate the jISI to evaluate JBSS performance.

W = np.moveaxis(transform, [0, 1, 2], [1, 0, 2])
print(f'joint_isi genvar: {_bss_isi(W, A)[1]}')

A jISI smaller than 0.05 means successful JBSS, i.e., the canonical variables are permuted and scaled versions of the true sources.

Contact

In case of questions, suggestions, problems etc., please send an email to isabell.lehmann@sst.upb.de, or open an issue here on Github.

Citing

If you use this package in an academic paper, please cite [1].

@article{Lehmann2025,
  title={A Comprehensive Guide to Multiset Canonical Correlation Analysis and its Application to Joint Blind Source Separation},
  author={Lehmann, Isabell and Gabrielson, Ben and Hasija, Tanuj and Adali, T{\"u}lay},
  journal={tba},
  year={tba},
  publisher={tba}
}

[1] I. Lehmann, B. Gabrielson, et al., A Comprehensive Guide to Multiset Canonical Correlation Analysis and its Application to Joint Blind Source Separation, submitted in 2025