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

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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https://hal.archives-ouvertes.fr/hal-02542653
Contributor : Zhang Sixin <>
Submitted on : Tuesday, April 14, 2020 - 6:24:14 PM
Last modification on : Tuesday, June 16, 2020 - 3:49:45 AM

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  • HAL Id : hal-02542653, version 1

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Sixin Zhang, Emmanuel Soubies, Cédric Févotte. On the Identifiability of Transform Learning for Non-negative Matrix Factorization. 2020. ⟨hal-02542653⟩

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