Did you get a chance to look at some similar papers?

[niravlekinwala]

During my PhD, I have tried to solve the same issue of using NMF based methods for source apportionment. Please check the papers out:

1. Main article titled "Generalised non-negative matrix factorisation for air pollution source apportionment" available at https://doi.org/10.1016/j.scitotenv.2022.156294
2. Software article titled "pyGNMF: A Python library for implementation of generalised non-negative matrix factorisation method" available at https://doi.org/10.1016/j.softx.2022.101257

GNMF method does not make any assumption about the structure of the uncertainty matrix and can also be a dense matrix.

Feel free to look at the mentioned papers. I have spent quite some time optimising the code so that it runs as fast as possible. However, I was not able complete the error estimation part in the pyGNMF method and thus was published without it.

[deronsmith]

Thank you for these resources @niravlekinwala. We will take a look at the GNMF algorithm that you developed in your article, as well as the pyGNMF package that you published.