The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
La conception et l'ajustement de la divergence dans les applications audio utilisant la factorisation matricielle non négative (NMF) restent un problème ouvert. Dans cette étude, pour résoudre ce problème, nous explorons une représentation de la divergence à l'aide de réseaux de neurones (NN). Au lieu de la divergence, notre approche étend l'algorithme de mise à jour multiplicative (MUA), qui estime les paramètres NMF, à l'aide de NN. La conception du MUA étendu intègre des NN, et le nouvel algorithme est appelé MUA profond (DeMUA) pour NMF. Alors que le DeMUA représente l'algorithme du NMF, il est intéressant de noter que la divergence est obtenue à partir du NN incorporé. De plus, nous proposons des guides théoriques pour concevoir le NN incorporé de telle sorte qu'il puisse être interprété comme une divergence. En concevant de manière appropriée le NN, les MUA basés sur les divergences existantes avec un seul hyper-paramètre peuvent être représentés par le DeMUA. Pour entraîner le DeMUA, nous l'avons appliqué au débruitage audio et à la séparation supervisée des signaux. Nos résultats expérimentaux montrent que l'architecture proposée peut apprendre le MUA et les divergences dans les tâches de débruitage et de séparation de la parole et que le MUA basé sur des divergences généralisées avec de multiples paramètres montre des performances favorables sur ces tâches.
Hiroki TANJI
Meiji University
Takahiro MURAKAMI
Meiji University
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Hiroki TANJI, Takahiro MURAKAMI, "Deep Multiplicative Update Algorithm for Nonnegative Matrix Factorization and Its Application to Audio Signals" in IEICE TRANSACTIONS on Fundamentals,
vol. E106-A, no. 7, pp. 962-975, July 2023, doi: 10.1587/transfun.2022EAP1098.
Abstract: The design and adjustment of the divergence in audio applications using nonnegative matrix factorization (NMF) is still open problem. In this study, to deal with this problem, we explore a representation of the divergence using neural networks (NNs). Instead of the divergence, our approach extends the multiplicative update algorithm (MUA), which estimates the NMF parameters, using NNs. The design of the extended MUA incorporates NNs, and the new algorithm is referred to as the deep MUA (DeMUA) for NMF. While the DeMUA represents the algorithm for the NMF, interestingly, the divergence is obtained from the incorporated NN. In addition, we propose theoretical guides to design the incorporated NN such that it can be interpreted as a divergence. By appropriately designing the NN, MUAs based on existing divergences with a single hyper-parameter can be represented by the DeMUA. To train the DeMUA, we applied it to audio denoising and supervised signal separation. Our experimental results show that the proposed architecture can learn the MUA and the divergences in sparse denoising and speech separation tasks and that the MUA based on generalized divergences with multiple parameters shows favorable performances on these tasks.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2022EAP1098/_p
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@ARTICLE{e106-a_7_962,
author={Hiroki TANJI, Takahiro MURAKAMI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Deep Multiplicative Update Algorithm for Nonnegative Matrix Factorization and Its Application to Audio Signals},
year={2023},
volume={E106-A},
number={7},
pages={962-975},
abstract={The design and adjustment of the divergence in audio applications using nonnegative matrix factorization (NMF) is still open problem. In this study, to deal with this problem, we explore a representation of the divergence using neural networks (NNs). Instead of the divergence, our approach extends the multiplicative update algorithm (MUA), which estimates the NMF parameters, using NNs. The design of the extended MUA incorporates NNs, and the new algorithm is referred to as the deep MUA (DeMUA) for NMF. While the DeMUA represents the algorithm for the NMF, interestingly, the divergence is obtained from the incorporated NN. In addition, we propose theoretical guides to design the incorporated NN such that it can be interpreted as a divergence. By appropriately designing the NN, MUAs based on existing divergences with a single hyper-parameter can be represented by the DeMUA. To train the DeMUA, we applied it to audio denoising and supervised signal separation. Our experimental results show that the proposed architecture can learn the MUA and the divergences in sparse denoising and speech separation tasks and that the MUA based on generalized divergences with multiple parameters shows favorable performances on these tasks.},
keywords={},
doi={10.1587/transfun.2022EAP1098},
ISSN={1745-1337},
month={July},}
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TY - JOUR
TI - Deep Multiplicative Update Algorithm for Nonnegative Matrix Factorization and Its Application to Audio Signals
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 962
EP - 975
AU - Hiroki TANJI
AU - Takahiro MURAKAMI
PY - 2023
DO - 10.1587/transfun.2022EAP1098
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E106-A
IS - 7
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - July 2023
AB - The design and adjustment of the divergence in audio applications using nonnegative matrix factorization (NMF) is still open problem. In this study, to deal with this problem, we explore a representation of the divergence using neural networks (NNs). Instead of the divergence, our approach extends the multiplicative update algorithm (MUA), which estimates the NMF parameters, using NNs. The design of the extended MUA incorporates NNs, and the new algorithm is referred to as the deep MUA (DeMUA) for NMF. While the DeMUA represents the algorithm for the NMF, interestingly, the divergence is obtained from the incorporated NN. In addition, we propose theoretical guides to design the incorporated NN such that it can be interpreted as a divergence. By appropriately designing the NN, MUAs based on existing divergences with a single hyper-parameter can be represented by the DeMUA. To train the DeMUA, we applied it to audio denoising and supervised signal separation. Our experimental results show that the proposed architecture can learn the MUA and the divergences in sparse denoising and speech separation tasks and that the MUA based on generalized divergences with multiple parameters shows favorable performances on these tasks.
ER -