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Split gradient method for informed non-negative matrix factorization

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01367330
Contributor : Matthieu Puigt <>
Submitted on : Thursday, September 15, 2016 - 10:55:52 PM
Last modification on : Tuesday, January 5, 2021 - 1:04:02 PM

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Robert Chreiky, Gilles Delmaire, Matthieu Puigt, Gilles Roussel, Dominique Courcot, et al.. Split gradient method for informed non-negative matrix factorization. 12th International Conference on Latent Variable Analysis and Signal Separation (LVA/ICA 2015), Aug 2015, Liberec, Czech Republic. pp.376-383, ⟨10.1007/978-3-319-22482-4_44⟩. ⟨hal-01367330⟩

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