matcouply 0.1.6

Regularized 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. For a quick introduction to coupled matrix factorization and PARAFAC2 see the online documentation.

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[gpl]

About

MatCoupLy is a Python library that adds support for coupled matrix factorization in TensorLy. For optimization, MatCoupLy uses alternating updates with the alternating direction method of multipliers (AO-ADMM), which allows you to fit coupled matrix factorization (and PARAFAC2) models with flexible constraints in any mode of your data [1, 2]. Currently, MatCoupLy supports the NumPy and PyTorch backends of TensorLy.

Example

Below is a simulated example, where a set of 15 non-negative coupled matrices are generated and decomposed using a non-negative PARAFAC2 factorization with an L1 penalty on C, constraining the maximum norm of the A and Bᵢ matrices and unimodality constraints on the component vectors in the Bᵢ matrices. For more examples, see the Gallery of examples in the online documentation.

import matplotlib.pyplot as plt
import numpy as np

from matcouply.data import get_simple_simulated_data
from matcouply.decomposition import cmf_aoadmm

noisy_matrices, cmf = get_simple_simulated_data(noise_level=0.2, random_state=1)
rank = cmf.rank
weights, (A, B_is, C) = cmf

# Decompose the dataset
estimated_cmf = cmf_aoadmm(
    noisy_matrices,
    rank=rank,
    non_negative=True,  # Constrain all components to be non-negative
    l1_penalty={2: 0.1},  # Sparsity on C
    l2_norm_bound=[1, 1, 0],  # Norm of A and B_i-component vectors less than 1
    parafac2=True,  # Enforce PARAFAC2 constraint
    unimodal={1: True},  # Unimodality (one peak) on the B_i component vectors
    constant_feasibility_penalty=True,  # Must be set to apply l2_norm_penalty (row-penalty) on A. See documentation for more details
    verbose=-1,  # Negative verbosity level for minimal (nonzero) printouts
    random_state=0,  # A seed can be given similar to how it's done in TensorLy
)

est_weights, (est_A, est_B_is, est_C) = estimated_cmf

# Code to display the results
def normalize(M):
    return M / np.linalg.norm(M, axis=0)

fig, axes = plt.subplots(2, 3, figsize=(5, 2))
axes[0, 0].plot(normalize(A))
axes[0, 1].plot(normalize(B_is[0]))
axes[0, 2].plot(normalize(C))

axes[1, 0].plot(normalize(est_A))
axes[1, 1].plot(normalize(est_B_is[0]))
axes[1, 2].plot(normalize(est_C))

axes[0, 0].set_title(r"$\mathbf{A}$")
axes[0, 1].set_title(r"$\mathbf{B}_0$")
axes[0, 2].set_title(r"$\mathbf{C}$")

axes[0, 0].set_ylabel("True")
axes[1, 0].set_ylabel("Estimated")

for ax in axes.ravel():
    ax.set_yticks([])  # Components can be aribtrarily scaled
for ax in axes[0]:
    ax.set_xticks([])  # Remove xticks from upper row

plt.savefig("figures/readme_components.png", dpi=300)

All regularization penalties (including regs list):
* Mode 0:
   - <'matcouply.penalties.L2Ball' with aux_init='random_uniform', dual_init='random_uniform', norm_bound=1, non_negativity=True)>
* Mode 1:
   - <'matcouply.penalties.Parafac2' with svd='truncated_svd', aux_init='random_uniform', dual_init='random_uniform', update_basis_matrices=True, update_coordinate_matrix=True, n_iter=1)>
   - <'matcouply.penalties.Unimodality' with aux_init='random_uniform', dual_init='random_uniform', non_negativity=True)>
   - <'matcouply.penalties.L2Ball' with aux_init='random_uniform', dual_init='random_uniform', norm_bound=1, non_negativity=True)>
* Mode 2:
   - <'matcouply.penalties.L1Penalty' with aux_init='random_uniform', dual_init='random_uniform', reg_strength=0.1, non_negativity=True)>
converged in 218 iterations: FEASIBILITY GAP CRITERION AND RELATIVE LOSS CRITERION SATISFIED

References

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

• [2]: Roald M, Schenker C, Calhoun VD, Adali T, Bro R, Cohen JE, Acar E An AO-ADMM approach to constraining PARAFAC2 on all modes (2022). Accepted for publication in SIAM Journal on Mathematics of Data Science, arXiv preprint arXiv:2110.01278.