A Generalization of Laplace Nonnegative Matrix Factorization and Its Multichannel Extension

Tanji, Hiroki; Murakami, Takahiro; Kamata, Hiroyuki

doi:10.1109/apsipaasc47483.2019.9023125

Cited by 1 publication

(4 citation statements)

References 25 publications

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“…The CPDF-based divergence was first proposed in [21] to interpret the divergence as a statistical model of the complex spectrogram. Recently, to generalize [21], divergences based on the symmetric 𝛼 stable [17], Student's 𝑡 [18], generalized Gaussian [19], and Bessel [20] distributions have been proposed. NMFs based on these divergences and their special cases are summarized in Table 1.…”

Section: Existing Divergences and Algorithmsmentioning

confidence: 99%

“…This is because these divergences generally depend on the scale of the observed matrix and provide a low-rank approximation We show the divergences and the CPDFs reconstructed from the trained NNs using Eqs. (17), (20), and (21) in Figs. 5 and 6.…”

Section: Sparse Denoisingmentioning

confidence: 99%

“…Various divergences have been proposed in the NMF literature [1,11,[14][15][16][17][18][19][20][21][22]. Of these, divergences [11,[15][16][17][18][19][20] that are generalized using hyper-parameters are promising because they allow the evaluation of various types of divergences in audio applications. For example, [11] introduced the Bregman divergence, which is parameterized by any strictly convex function.…”

Section: Introductionmentioning

confidence: 99%

“…The alpha-beta divergence [15] parameterized by two hyper-parameters is a well-known generalization. In addition, generalized statistical models of the observed complex spectrogram have been proposed in [17][18][19][20] not only to generalize the divergence but also to obtain a statistical interpretation of the divergence. In these models, the divergence is derived from the complex probability distribution function (CPDF) of the time-frequency bin of the complex spectrogram.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Deep Multiplicative Update Algorithm for Nonnegative Matrix Factorization and Its Application to Audio Signals

Tanji

Murakami

2023

IEICE Trans. Fundamentals

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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.

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