{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-quasi-newton-algorithm-on-the-orthogonal","title":"A Quasi-Newton algorithm on the orthogonal manifold for NMF with transform learning","arxiv_id":"1811.02225","date":"2018-11-06","proceeding":null,"authors":["Pierre Ablin","Dylan Fagot","Herwig Wendt","Alexandre Gramfort","Cédric Févotte"],"abstract":"Nonnegative matrix factorization (NMF) is a popular method for audio spectral\nunmixing. While NMF is traditionally applied to off-the-shelf time-frequency\nrepresentations based on the short-time Fourier or Cosine transforms, the\nability to learn transforms from raw data attracts increasing attention.\nHowever, this adds an important computational overhead. When assumed orthogonal\n(like the Fourier or Cosine transforms), learning the transform yields a\nnon-convex optimization problem on the orthogonal matrix manifold. In this\npaper, we derive a quasi-Newton method on the manifold using sparse\napproximations of the Hessian. Experiments on synthetic and real audio data\nshow that the proposed algorithm out-performs state-of-the-art first-order and\ncoordinate-descent methods by orders of magnitude. A Python package for fast\nTL-NMF is released online at https://github.com/pierreablin/tlnmf.","url_abs":"http://arxiv.org/abs/1811.02225v1","url_pdf":"http://arxiv.org/pdf/1811.02225v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"a-quasi-newton-algorithm-on-the-orthogonal","repo_url":"https://github.com/pierreablin/tlnmf","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}