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.
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 -