Positive Matrix Factorization (PMF; Paatero, 1997) is a factorization method commonly used in the environmental sciences since unlike nonnegative matrix factorization (NMF), it utilizes known uncertainties to weight the residuals throughout the optimization. It is potentially an algorithm that could see wide-spread use; however, the only two commonly used algorithms are proprietary (Paatero’s costs ~$650 and you have to email him to get it…). I’ve thought about implementing it in Python for a while, but haven’t really had a reason to for my own personal research (I’m a PhD candidate at MIT).
I’ve been an occasional Julia user since ~v0.4 when I took 18.0651 and thought Julia would be the optimal choice since I seem to recall it handles sparse matrices well. Is there anyone with more of a math and/or Julia background that would be interested in co-developing a Julia package for this?