A quasi-Newton Algorithm on the Orthogonal Manifold for NMF with Transform Learning

Pierre Ablin, Dylan Fagot, Herwig Wendt, Alexandre Gramfort, Cedric Fevotte
2019 ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
Nonnegative matrix factorization (NMF) is a popular method for audio spectral unmixing. While NMF is traditionally applied to off-the-shelf time-frequency representations based on the short-time Fourier or Cosine transforms, the ability to learn transforms from raw data attracts increasing attention. However, this adds an important computational overhead. When assumed orthogonal (like the Fourier or Cosine transforms), learning the transform yields a nonconvex optimization problem on the
more » ... nal matrix manifold. In this paper, we derive a quasi-Newton method on the manifold using sparse approximations of the Hessian. Experiments on synthetic and real audio data show that the proposed algorithm outperforms stateof-the-art first-order and coordinate-descent methods by orders of magnitude in terms of speed. A Python package for fast TL-NMF is released online at https://github.com/pierreablin/tlnmf.
doi:10.1109/icassp.2019.8683291 dblp:conf/icassp/AblinFWGF19 fatcat:z5h4nucvy5fbvi6e3cfvjbau6y