Software for deep nonnegative matrix factorization with the beta-divergence:

This repository contains the software for deep beta-NMF with and without minimum-volume regularization, for beta={1,3/2}.

This MATLAB software reproduces the results from the following paper:

@misc{leplat2023deep,
      title={Deep Nonnegative Matrix Factorization with Beta Divergences}, 
      author={Valentin Leplat and Le Thi Khanh Hien and Akwum Onwunta and Nicolas Gillis},
      year={2023},
      eprint={2309.08249},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}

Acknowledgements

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

Content

/Libraries : contains helpful libaries; in particular Libraries/nmfbook-master/ contains the code of the NMF toolbox from https://gitlab.com/ngillis/nmfbook/
/demos : contains demo files that produce tables and figures.
main.m : codes that allow to run desired demos.
/Utils : contains helpful files and MatLab routines to run the demos.

Demo file

A demo is available. To proceed, please type "1", "2" or "3" when running the main.m file.

Tuning the parameters

There are several parameters that you can choose:

The ranks r's of the deep decomposition
The number of iterations for the init stage and the proposed Algorithms 1 and 2
The accuracy for the computation of the optimal Lagrangian multipliers for MU to respect normalization constraints,
Parameters for ADMM procedure from Algorithm 2: rho, threshold and maximum number of iterations. Here, we allow the user to consider a new accelerated version of the ADMM procedure, see flag "options.accADMM"
Parameters for min-volume: \alpha_tilde helps to setup the weights \alpha_l for the min-vol regualirzations terms. \alpha_tilde vector corresponds to the initial and desired ratio between the min-vol terms w.r.t. to the general objective function.

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

Reproduce figures and results from the paper

To do so, you need to run the main.m file. Here, a menu is available and allows you to choose which figure or table you want to generate. Each number in the table below corresponds to a set of figures.