Block-Majorization-Minimization-with-Extrapolation

Block Majorization Minimization with Extrapolation and Application to $\beta$-NMF

This MATLAB software reproduces the results from the following paper:

@article{LeThiKhanhHien_BMMex2024,
      title={Block Majorization Minimization with Extrapolation and Application to $\beta$-{NMF}}, 
      author={Le Thi Khanh Hien and Valentin Leplat and Nicolas Gillis},
      year={2024},
      journal={arXiv preprint arXiv:2401.06646} 
}

See https://arxiv.org/abs/2401.06646

Acknowledgements

The baseline algorithms used in the manuscript are courtesy of their respective authors.

Content

/Libraries : contains helpful libaries; in particular Libraries/group_robust_NMF/ contains the code of group robust NMF proposed in Ref[1] and Algorithm 2 from Ref[2] aimed at solving min-vol KL NMF.
/Datasets : contains test data sets.
/Utils : contains helpful files and MatLab routines to run the demos.
/Methods: contains the MatLab implementations of the Algorithms developped in the paper.
test files detailed in next Section

Test files

Test files are available. To proceed, open and start one of the following files:

test_Example_in_Intro_CBCL.m : run demo for generating Figure 1 from Section 1.3 of the paper.
test_Hyperspectral_Images_betaNMF32.m : run demo for $\beta=3/2$-NMF for hyperspectral imaging, see Section 5.1 of the paper.
test_Images_DocClassification.m : run benchmark for KL-NMF for Images data sets and document classification (data sets specified within the file), see section 5.1 of th paper.
test_Audio_minvolKLNMF.m : run demo for min-vol KL NMF for blind audio SS tasks, section 5.2 of the paper.

Tuning the parameters

There are several parameters that you can choose:

$r$: the factorization rank
$\tilde{\lambda}$: the relative weight parameter for min-vol penalty, see Appendix B.3 for more details
the maximum computation time for benchmarking

For benchmarked approaches, the parameters have been tuned according to the original works:

for audio SS tasks; we followed Ref [3].
for cbcl and document classification; we followed Ref [4].

References:

[1]: C. Févotte and N. Dobigeon, "Nonlinear Hyperspectral Unmixing With Robust Nonnegative Matrix Factorization," in IEEE Transactions on Image Processing, vol. 24, no. 12, pp. 4810-4819, Dec. 2015, doi: 10.1109/TIP.2015.2468177.

[2]: V. Leplat, N. Gillis and J. Idier, "Multiplicative Updates for NMF with β-Divergences under Disjoint Equality Constraints", SIAM J. on Matrix Analysis and Applications 42 (2), 730-752, 2021.

[3]: V. Leplat, N. Gillis and A.M.S. Ang, "Blind Audio Source Separation with Minimum-Volume Beta-Divergence NMF", IEEE Transactions on Signal Processing 68, pp. 3400-3410, 2020.

[4]: L.T.K. Hien and N. Gillis. "Algorithms for nonnegative matrix factorization with the Kullback-Leibler divergence." Journal of Scientific Computing, (87):93, 2021.

vleplat / BMMe