On the Relationships between Transform-Learning NMF and Joint-Diagonalization

• URL: http://arxiv.org/abs/2112.05664v1
• Date: Fri, 10 Dec 2021 16:52:15 GMT
• Title: On the Relationships between Transform-Learning NMF and Joint-Diagonalization
• Authors: Sixin Zhang, Emmanuel Soubies, and C\'edric F\'evotte
• Abstract summary: Non-negative matrix factorization with transform learning (TL-NMF) is a recent idea that aims at learning data representations suited to NMF. We show that, when the number of data realizations is sufficiently large, TL-NMF can be replaced by a two-step approach.
• Score: 5.155159655787271
• License: http://creativecommons.org/licenses/by/4.0/
• 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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