Complex NMF: A new sparse representation for acoustic signals

Kameoka, Hirokazu; Ono, Nobutaka; Kashino, Kunio; Sagayama, Shigeki

doi:10.1109/icassp.2009.4960364

Cited by 130 publications

(137 citation statements)

References 7 publications

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“…The inequality (35) has previously been derived, less the group notation, using Young's inequality [48], and through calculating a quadratic function that is tangent to the concave left hand side at the current estimate [49] [44]. The second term of the right hand side in (35) is a constant in terms of y[j] as it is given in terms of the auxiliary variable, allowing the auxiliary function for the β 2 penalty to be given as…”

Section: B Backwards Eliminationmentioning

confidence: 99%

Non-Negative Group Sparsity with Subspace Note Modelling for Polyphonic Transcription

O'Hanlon

Nagano

Keriven

et al. 2016

IEEE/ACM Trans. Audio Speech Lang. Process.

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Abstract-Automatic Music Transcription (AMT) can be performed by deriving a pitch-time representation through decomposition of a spectrogram with a dictionary of pitch-labelled atoms. Typically, Non-negative Matrix Factorisation (NMF) methods are used to decompose magnitude spectrograms. One atom is often used to represent each note. However, the spectrum of a note may change over time. Previous research considered this variability using different atoms to model specific parts of a note, or large dictionaries comprised of datapoints from the spectrograms of full notes. In this paper the use of subspace modelling of note spectra is explored, with group sparsity employed as a means of coupling activations of related atoms into a pitched subspace.Stepwise and gradient-based methods for non-negative group sparse decompositions are proposed. Finally, a group sparse NMF approach is used to tune a generic harmonic subspace dictionary, leading to improved NMF-based AMT results.

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Section: B Backwards Eliminationmentioning

confidence: 99%

Non-Negative Group Sparsity with Subspace Note Modelling for Polyphonic Transcription

O'Hanlon

Nagano

Keriven

et al. 2016

IEEE/ACM Trans. Audio Speech Lang. Process.

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“…Nonnegative matrices T and V, whose elements are t ik ≥ 0 and v kj ≥ 0, have sizes of I × K and K × J, respectively. If we preserve the phase information of X, complex NMF [4] can be applied. The generative model can be written as…”

Section: Nmf and Complex Nmfmentioning

confidence: 99%

“…Complex NMF [4] takes account of the phase information xij /|xij |, which is discarded with standard NMF. It improves the analysis accuracy by faithfully obeying the mixing process in the complex domain.…”

Section: Introductionmentioning

confidence: 99%

Formulations and algorithms for multichannel complex NMF

Sawada

Kameoka

Araki

2011

2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This paper studies some formulations and algorithms for the multichannel extension of nonnegative matrix factorization (NMF). We model the inter-channel characteristics of each NMF basis, including both the amplitude ratios and the phase differences on a channel pair. The learned inter-channel characteristics provide useful information for binding each NMF basis to each source component in such a situation that multiple sources are mixed in a convolutive manner and observed at multiple microphones. Effective optimization algorithms based on majorization are derived by using properly designed auxiliary functions. Experimental results show that the algorithms converged favorably regardless of the initialization.

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“…While this approach provides the means to interpret NMF as a probabilistic process, some of these assumptions are often not met using realworld recordings [9]. Furthermore, a variant referred to as complex-NMF was introduced, which operates on complex-valued spectrograms [10]. While the relaxation of the strict non-negativity constraints used in standard NMF leads to more freedom in the signal model, it can also lower the robustness of the learning process in some cases.…”

Section: Introductionmentioning

confidence: 99%

Accounting for phase cancellations in non-negative matrix factorization using weighted distances

Ewert

Plumbley

Sandler

2014

2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Techniques based on non-negative matrix factorization (NMF) have been successfully used to decompose a spectrogram of a music recording into a dictionary of templates and activations. While advanced NMF variants often yield robust signal models, there are usually some inaccuracies in the factorization since the underlying methods are not prepared for phase cancellations that occur when sounds with similar frequency are mixed. In this paper, we present a novel method that takes phase cancellations into account to refine dictionaries learned by NMF-based methods. Our approach exploits the fact that advanced NMF methods are often robust enough to provide information about how sound sources interact in a spectrogram, where they overlap, and thus where phase cancellations could occur. Using this information, the distances used in NMF are weighted entry-wise to attenuate the influence of regions with phase cancellations. Experiments on full-length, polyphonic piano recordings indicate that our method can be successfully used to refine NMF-based dictionaries.

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Complex NMF: A new sparse representation for acoustic signals

Cited by 130 publications

References 7 publications

Non-Negative Group Sparsity with Subspace Note Modelling for Polyphonic Transcription

Non-Negative Group Sparsity with Subspace Note Modelling for Polyphonic Transcription

Formulations and algorithms for multichannel complex NMF

Accounting for phase cancellations in non-negative matrix factorization using weighted distances

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