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International Conference on Latent Variable Analysis and Signal Separation

LVA/ICA 2018: Latent Variable Analysis and Signal Separation pp 89–98Cite as

Nonnegative PARAFAC2: A Flexible Coupling Approach

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10891))

Abstract

Modeling variability in tensor decomposition methods is one of the challenges of source separation. One possible solution to account for variations from one data set to another, jointly analysed, is to resort to the PARAFAC2 model. However, so far imposing constraints on the mode with variability has not been possible. In the following manuscript, a relaxation of the PARAFAC2 model is introduced, that allows for imposing nonnegativity constraints on the varying mode. An algorithm to compute the proposed flexible PARAFAC2 model is derived, and its performance is studied on both synthetic and chemometrics data.

Research funded by F.R.S.-FNRS incentive grant for scientific research n\(^\text {o}\) F.4501.16.

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Notes

  1. 1.

    Alternating optimization may be avoided using an all-at-once method but the problem of satisfying the nonnegativity constraints still remains.

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Acknowledgements

The authors wish to thank Nicolas Gillis for helpful discussions on alternatives to the flexible coupling approach for computing nonnegative PARAFAC2.

Author information

Authors and Affiliations

  1. Departement of Mathematics and Operational Research, Faculté polytechnique, Université de Mons, Rue de Houdain 9, Mons, Belgium

    Jeremy E. Cohen & Rasmus Bro

  2. Departement of Food Science, University of Copenhagen, Rolighedsvej 26 1958 Frederiksberg C, Copenhagen, Denmark

    Jeremy E. Cohen & Rasmus Bro

Authors
  1. Jeremy E. Cohen
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  2. Rasmus Bro
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Corresponding author

Correspondence to Jeremy E. Cohen .

Editor information

Editors and Affiliations

  1. Paul Sabatier University, Toulouse, France

    Yannick Deville

  2. Bar-Ilan University, Ramat Gan, Israel

    Sharon Gannot

  3. University of Surrey, Guildford, United Kingdom

    Russell Mason

  4. University of Surrey, Guildford, United Kingdom

    Mark D. Plumbley

  5. University of Surrey, Guildford, United Kingdom

    Dominic Ward

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Cohen, J.E., Bro, R. (2018). Nonnegative PARAFAC2: A Flexible Coupling Approach. In: Deville, Y., Gannot, S., Mason, R., Plumbley, M., Ward, D. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2018. Lecture Notes in Computer Science(), vol 10891. Springer, Cham. https://doi.org/10.1007/978-3-319-93764-9_9

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  • DOI: https://doi.org/10.1007/978-3-319-93764-9_9

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-93763-2

  • Online ISBN: 978-3-319-93764-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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