Nonnegative Matrix Factorization (NMF) with Heteroscedastic Uncertainties and Missing data

Abstract

Dimensionality reduction and matrix factorization techniques are important and useful machine-learning techniques in many fields. Nonnegative matrix factorization (NMF) is particularly useful for spectral analysis and image processing in astronomy. I present the vectorized update rules and an independent proof of their convergence for NMF with heteroscedastic measurements and missing data. I release a Python implementation of the rules and use an optical spectroscopic dataset of extragalactic sources as an example for demonstration. A future paper will present results of applying the technique to image processing of planetary disks.

Vectorized update rules for NMF with heteroscedastic measurements and the proof. The code NonnegMFPy is available at https://github.com/guangtunbenzhu/NonnegMFPy and can be installed through PyPI. Comments are most welcome