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Title: Split gradient method for informed non-negative matrix factorization
Authors: Chreiky, Robert
Delmaire, Gilles
Puigt, Matthieu
Roussel , Gilles
Courcot, Dominique
Abche, Antoine 
Affiliations: Department of Electrical Engineering 
Keywords: Informed source separation
Non-negative matrix factorization
Split gradient
Source apportionment
Issue Date: 2015
Part of: Latent Variable Analysis and Signal Separation
Start page: 376
End page: 383
Conference: International Conference on Latent Variable Analysis and Signal Separation (12th : 25-28 August, 2015 : Liberec Czech Republic) 
Recently, some informed Non-negative Matrix Factorization (NMF) methods were introduced in which some a priori knowledge (i.e., experts 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.
Type: Conference Paper
Appears in Collections:Department of Electrical Engineering

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