Nonnegative Matrix Factorization with the Itakura-Saito Divergence: With Application to Music Analysis

By Cédric Févotte, Nancy Bertin, Jean-Louis Durrieu. Neural Computation, 2009

1,233 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/34e86b693642b41e60e41f7a53bd9821764bda7c

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In Signal Processing

Citations in the corpus

Towards Scaling Up Classification-Based Speech Separation (2013, background): “, [15], [36]), but statistical source models are usually required or need to be adapted.”
Learning to Separate Object Sounds by Watching Unlabeled Video (2018, methodology): “Popular approaches include Independent Component Analysis (ICA) [36], sparse decomposition [78], Computational Auditory Scene Analysis (CASA) [21], non-negative matrix factorization (NMF) [23,24,46,69], probabilistic latent variable models [34,61], and deep learning [32,35].”
Structured sparsity through convex optimization (2011, background): “Learning on matrices - Source separation • Single microphone (Benaroya et al., 2006; Févotte et al., 2009)”
Global and Local Simplex Representations for Multichannel Source Separation (2020, background): “be decomposed as a multiplication of two nonnegative components, namely, a dictionary of recurring patterns and activation coefficients [10]–[14].”
A Consolidated Perspective on Multimicrophone Speech Enhancement and Source Separation (2017, neutral): “(cid:98) (cid:98) • M-step : Update R j ( f ) as in (112), and update b jk ( f ) and h jk ( n ) via multiplicative update (MU) rules [281] NMF structuring of source variances σ 2 s j ( n,f ) as in (137) can be represented as a factorization of F × N nonnegative matrix V j [ σ 2 s j ( n,f )] n,f…”
Beyond NMF: Time-Domain Audio Source Separation without Phase Reconstruction (2013, methodology): “(26) This algorithm is theoretically guaranteed to converge and in fact a similar idea was used for IS-NMF [18].”
Online Learning for Matrix Factorization and Sparse Coding (2009, background): “…tasks such as image denoising (Elad and Aharon, 2006; Mairal et al., 2008b), texture synthesis (Peyr´e, 2009) and audio processing (Grosse et al., 2007; F´evotte et al., 2009; Zibulevsky and Pearlmutter, 2001), as well as higher-level tasks such as image classiﬁcation (Raina et al., 2007; Mairal…”
Families of Alpha- Beta- and Gamma- Divergences: Flexible and Robust Measures of Similarities (2010, methodology): “This is especially important in the scenario in which the coefficients of p have a large dynamic range, such as in short-term audio spectra [30,76,79].”
New Era for Robust Speech Recognition (2017, methodology): “t; f / after each expectation step, following an approach first applied in image segmentation [12].”
Contextual Bandits with Latent Confounders: An NMF Approach (2016, background): “Online Matrix factorization : The non-negative matrix factorization (NMF) problem has generated a lot of interest in the area of semi-supervised topic modeling.”
Primal-dual algorithms for non-negative matrix factorization with the Kullback-Leibler divergence (2014, methodology): ““My Heart (Will Always Lead Me Back to You)” [5]”
Algorithms for Nonnegative Matrix Factorization with the β-Divergence (2010, methodology): “As discussed in (Févotte et al., 2009), K was set to 6 so as to retrieve in W the individual spectra of each of the 4 notes and supplementary spectra corresponding to transients and residual noise.”
Online Nonnegative Matrix Factorization With Robust Stochastic Approximation (2012, methodology): “According to [33], the problem (33) can be solved by iteratively updated ht from a random initial point through the following multiplicative rule until convergence: ht ← ht ⊗ (W T t ×( vt/(Wt ht )2))/(W T t ×(1/Wt ht )), where ⊗ signifies the element-wise product.”
Multichannel Audio Source Separation With Deep Neural Networks (2016, methodology): “2) The Kullback-Leibler (KL) divergence [38] is expressed as It is also a popular choice for NMF-based audio source separation [35] and has been shown to be effective for DNN training [13].”
Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing (2019, methodology): “y a ﬁltering process similar to the classical Wiener ﬁltering is performed for magnitude spectrogram recovery. To determine W and H from M, one may consider solving the following optimization problem [63]: Wc;Hb= arg min W0;H0 D(MjWH)+kHk1; (23) where D is the -divergence, which can be considered as”