---
OA_type: closed access
_id: '18327'
abstract:
- lang: eng
  text: 'Source separation is a widely studied problem in signal processing. Despite
    the permanent progress reported in the literature it is still considered a significant
    challenge. This chapter first reviews the use of non-negative matrix factorization
    (NMF) algorithms for solving source separation problems, and proposes a new way
    for the supervised training in NMF. Matrix factorization methods have received
    a lot of attention in recent year in the audio processing community, producing
    particularly good results in source separation. Traditionally, NMF algorithms
    consist of two separate stages: a training stage, in which a generative model
    is learned; and a testing stage in which the pre-learned model is used in a high
    level task such as enhancement, separation, or classification. As an alternative,
    we propose a task-supervised NMF method for the adaptation of the basis spectra
    learned in the first stage to enhance the performance on the specific task used
    in the second stage. We cast this problem as a bilevel optimization program efficiently
    solved via stochastic gradient descent. The proposed approach is general enough
    to handle sparsity priors of the activations, and allow non-Euclidean data terms
    such as β-divergences. The framework is evaluated on speech enhancement.'
alternative_title:
- Applied and Numerical Harmonic Analysis
article_processing_charge: No
author:
- first_name: Pablo
  full_name: Sprechmann, Pablo
  last_name: Sprechmann
- first_name: Alexander
  full_name: Bronstein, Alexander
  id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
  last_name: Bronstein
  orcid: 0000-0001-9699-8730
- first_name: Guillermo
  full_name: Sapiro, Guillermo
  last_name: Sapiro
citation:
  ama: 'Sprechmann P, Bronstein AM, Sapiro G. Supervised non-negative matrix factorization
    for audio source separation. In: <i>Excursions in Harmonic Analysis, Volumne 4</i>.
    1st ed. Cham: Springer Nature; 2015:407-420. doi:<a href="https://doi.org/10.1007/978-3-319-20188-7_16">10.1007/978-3-319-20188-7_16</a>'
  apa: 'Sprechmann, P., Bronstein, A. M., &#38; Sapiro, G. (2015). Supervised non-negative
    matrix factorization for audio source separation. In <i>Excursions in Harmonic
    Analysis, Volumne 4</i> (1st ed., pp. 407–420). Cham: Springer Nature. <a href="https://doi.org/10.1007/978-3-319-20188-7_16">https://doi.org/10.1007/978-3-319-20188-7_16</a>'
  chicago: 'Sprechmann, Pablo, Alex M. Bronstein, and Guillermo Sapiro. “Supervised
    Non-Negative Matrix Factorization for Audio Source Separation.” In <i>Excursions
    in Harmonic Analysis, Volumne 4</i>, 1st ed., 407–20. Cham: Springer Nature, 2015.
    <a href="https://doi.org/10.1007/978-3-319-20188-7_16">https://doi.org/10.1007/978-3-319-20188-7_16</a>.'
  ieee: 'P. Sprechmann, A. M. Bronstein, and G. Sapiro, “Supervised non-negative matrix
    factorization for audio source separation,” in <i>Excursions in Harmonic Analysis,
    Volumne 4</i>, 1st ed., Cham: Springer Nature, 2015, pp. 407–420.'
  ista: 'Sprechmann P, Bronstein AM, Sapiro G. 2015.Supervised non-negative matrix
    factorization for audio source separation. In: Excursions in Harmonic Analysis,
    Volumne 4. Applied and Numerical Harmonic Analysis, , 407–420.'
  mla: Sprechmann, Pablo, et al. “Supervised Non-Negative Matrix Factorization for
    Audio Source Separation.” <i>Excursions in Harmonic Analysis, Volumne 4</i>, 1st
    ed., Springer Nature, 2015, pp. 407–20, doi:<a href="https://doi.org/10.1007/978-3-319-20188-7_16">10.1007/978-3-319-20188-7_16</a>.
  short: P. Sprechmann, A.M. Bronstein, G. Sapiro, in:, Excursions in Harmonic Analysis,
    Volumne 4, 1st ed., Springer Nature, Cham, 2015, pp. 407–420.
date_created: 2024-10-15T11:20:53Z
date_published: 2015-10-30T00:00:00Z
date_updated: 2024-10-22T08:09:36Z
day: '30'
doi: 10.1007/978-3-319-20188-7_16
edition: '1'
extern: '1'
language:
- iso: eng
month: '10'
oa_version: None
page: 407-420
place: Cham
publication: Excursions in Harmonic Analysis, Volumne 4
publication_identifier:
  eisbn:
  - '9783319201887'
  eissn:
  - 2296-5017
  isbn:
  - '9783319201870'
  issn:
  - 2296-5009
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Supervised non-negative matrix factorization for audio source separation
type: book_chapter
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2015'
...