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arXiv · 2112.05664

Leveraging Joint-Diagonalization in Transform-Learning NMF

Sixin Zhang·Emmanuel Soubies·Cédric Févotte
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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.

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Sixin Zhang, Emmanuel Soubies, Cédric Févotte. 2021-12-10. Leveraging Joint-Diagonalization in Transform-Learning NMF. https://doi.org/10.1109/tsp.2022.3188177

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