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Journal Articles IEEE Transactions on Signal Processing Year : 2022

Leveraging Joint-Diagonalization in Transform-Learning NMF

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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) is a recent idea that aims at learning data representations suited to NMF. In this work, we relate TL-NMF to the classical matrix joint-diagonalization (JD) problem. We show that, when the number of data realizations is sufficiently large, TL-NMF can be replaced by a two-step approach -- termed as JD+NMF -- that estimates the transform through JD, prior to NMF computation. In contrast, we found that when the number of data realizations is limited, not only is JD+NMF no longer equivalent to TL-NMF, but the inherent low-rank constraint of TL-NMF turns out to be an essential ingredient to learn meaningful transforms for NMF.

Dates and versions

hal-03481041 , version 1 (15-12-2021)

Licence

Attribution - CC BY 4.0

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Cite

Sixin Zhang, Emmanuel Soubies, Cédric Févotte. Leveraging Joint-Diagonalization in Transform-Learning NMF. IEEE Transactions on Signal Processing, 2022, ⟨10.1109/TSP.2022.3188177⟩. ⟨hal-03481041⟩
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