matcouply 0.0.1

Regularised coupled matrix factorisation with AO-ADMM

Learning coupled matrix factorizations with Python

MatCoupLy is a Python library for learning coupled matrix factorizations with flexible constraints and regularization with Python.

Installation

To install MatCoupLy and all MIT-compatible dependencies from PyPI, you can run

pip install matcouply

If you also want to enable total variation regularization, you need to install all components, which comes with a GPL-v3 lisence

pip install matcouply[all]

About

MatCoupLy uses AO-ADMM to fit constrained and regularised coupled matrix factorization (and PARAFAC2) models. It uses the alternating updates with the alternating direction method of multipliers (AO-ADMM) algorithm, which is very flexible in terms of constraints [1, 2]

Example

Below is a simulated example, where a set of three random non-negative coupled matrices are generated and decomposed using a non-negative PARAFAC2 factorization with both L1 and L2 penalty functions.

from matcouply import cmf_aoadmm
from matcouply.random import random_coupled_matrices

simulated_components = random_coupled_matrices(rank=3, shapes=((40, 25), (35, 25), (19, 25)))
simulated_data = simulated_components.to_matrices()

estimated_cmf, aux_vars, dual_vars = cmf_aoadmm(
    simulated_data,
    rank=3,
    non_negative=True,
    l1_penalty=[0.1, 0.2, 0.1],
    l2_penalty={2: 1},
    parafac2=True
)

est_weights, (est_A, est_B_is, est_C) = estimated_cmf

References

• [1]: Roald M, Schenker C, Cohen JE, Acar E. PARAFAC2 AO-ADMM: Constraints in all modes. EUSIPCO (2021).

• [2]: Roald M, Schenker C, Bro R, Cohen JE, Acar E. An AO-ADMM approach to constraining PARAFAC2 on all modes (2021). arXiv preprint arXiv:2110.01278.