Non-negative matrix factorization

[sjfleming]

Implement NMF.

Uses the algorithm of Mairal et al. from their online learning paper.

Current issues:

• Find a good solver for non-negative least squares regression
  • Mairal et al. recommend LARS (least angle)
  • Gao et al. (Welch group) recommend ANLS (but their implementation is in R)
  • Others use HALS and BPP (including nmf-torch package)
• Benchmark against existing algorithms (https://pypi.org/project/nmf-torch/)
  • Complicated by the fact that NMF is non-convex
• Implement cNMF

Looking forward

• Think about implementing different kinds of losses (other than L2 Frobenius norm), especially beta divergences, because the beta=1 beta divergence loss turns NMF into Poisson NMF (this is mentioned in the original Lee and Seung paper I think)