Split Gradient Method for Informed Non-negative Matrix Factorization

  • Robert Chreiky
  • Gilles Delmaire
  • Matthieu Puigt
  • Gilles Roussel
  • Dominique Courcot
  • Antoine Abche
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9237)


Recently, some informed Non-negative Matrix Factorization (NMF) methods were introduced in which some a priori knowledge (i.e., expert’s knowledge) were taken into account in order to improve the separation process. This knowledge was expressed as known components of one factor, namely the profile matrix. Also, the sum-to-one property of the profile matrix was taken into account by an appropriate sequential normalization. However, our previous approach was unable to check both constraints at the same time. In this work, a new parametrization is proposed which takes into consideration both constraints simultaneously by incorporating a new unconstrained matrix. From this parameterization, new updates rules are introduced which are based on the framework of the Split Gradient Method by Lantéri et al. The cost function is defined in terms of a weighted Frobenius norm and the developed rules involve a new shift in order to ensure the non-negativity property. Simulations on a noisy source apportionment problem show the relevance of the proposed method.


Informed source separation Non-negative matrix factorization Split gradient Source apportionment 



This work was funded by the “ECUME” project granted by the DREAL Nord Pas de Calais Agency.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Robert Chreiky
    • 1
    • 2
  • Gilles Delmaire
    • 1
  • Matthieu Puigt
    • 1
  • Gilles Roussel
    • 1
  • Dominique Courcot
    • 3
  • Antoine Abche
    • 2
  1. 1.LISICULCO, Université Lille Nord de FranceCalaisFrance
  2. 2.University of BalamandKouraLebanon
  3. 3.UCEIVULCO, Université Lille Nord de FranceDunkerqueFrance

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