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Nonnegative matrix factorization (NMF) is a popular method for audio spectralunmixing. While NMF is traditionally applied to off-the-shelf time-frequencyrepresentations based on the short-time Fourier or Cosine transforms, theability 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 anon-convex optimization problem on the orthogonal matrix manifold. In thispaper, we derive a quasi-Newton method on the manifold using sparseapproximations of the Hessian. Experiments on synthetic and real audio datashow that the proposed algorithm out-performs state-of-the-art first-order andcoordinate-descent methods by orders of magnitude. A Python package for fastTL-NMF is released online at https://github.com/pierreablin/tlnmf.

A Quasi-Newton algorithm on the orthogonal manifold for NMF with transform learning