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Journal Articles IEEE Signal Processing Letters Year : 2020

On the Identifiability of Transform Learning for Non-negative Matrix Factorization

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1
Sixin Zhang
  • Function : Author
  • PersonId : 745281
  • IdHAL : zhang-sixin
Emmanuel Soubies
Cédric Févotte

Abstract

Non-negative matrix factorization with transform learning (TL-NMF) aims at estimating a short-time orthogonal transform that projects temporal data into a domain that is more amenable to NMF than off-the-shelf time-frequency transforms. In this work, we study the identifiability of TL-NMF under the Gaussian composite model. We prove that one can uniquely identify row-spaces of the orthogonal transform by optimizing the likelihood function of the model. This result is illustrated on a toy source separation problem which demonstrates the ability of TL-NMF to learn a suitable orthogonal basis.
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Dates and versions

hal-02542653 , version 1 (14-04-2020)
hal-02542653 , version 2 (25-07-2020)
hal-02542653 , version 3 (18-08-2020)
hal-02542653 , version 4 (02-07-2022)
hal-02542653 , version 5 (23-08-2022)

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Sixin Zhang, Emmanuel Soubies, Cédric Févotte. On the Identifiability of Transform Learning for Non-negative Matrix Factorization. IEEE Signal Processing Letters, 2020, 27, pp.1555 - 1559. ⟨10.1109/LSP.2020.3020431⟩. ⟨hal-02542653v5⟩
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