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A Regularized Nonnegative Third Order Tensor decomposition Using a Primal-Dual Projected Gradient Algorithm: Application to 3D Fluorescence Spectroscopy

  • Karima El Qate
  • Mohammed El Rhabi
  • Abdelilah Hakim
  • Eric Moreau
  • Nadàge Thirion-Moreau
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11010)

Abstract

This paper investigates the use of Primal-Dual optimization algorithms on multidimensional signal processing problems. The data blocks interpreted in a tensor way can be modeled by means of multi-linear decomposition. Here we will focus on the Canonical Polyadic Decomposition (CPD), and we will present an application to fluorescence spectroscopy using this decomposition. In order to estimate the factors or latent variables involved in these decompositions, it is usual to use criteria optimization algorithms. A classical cost function consists of a measure of the modeling error (fidelity term) to which a regularization term can be added if necessary. Here, we consider one of the most efficient optimization methods, Primal-Dual Projected Gradient.

The effectiveness and the robustness of the proposed approach are shown through numerical examples.

Keywords

Constrained optimization Nonnegative tensor decomposition Primal-Dual Regularization Projected gradient 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Karima El Qate
    • 1
  • Mohammed El Rhabi
    • 2
  • Abdelilah Hakim
    • 1
  • Eric Moreau
    • 3
  • Nadàge Thirion-Moreau
    • 3
  1. 1.LAMAI, FSTG MarrakechUniversity of Cady AyyadMarrakeshMorocco
  2. 2.Applied Mathematics and Computer Science DepartmentEcole des Ponts ParisTech (ENPC)ParisFrance
  3. 3.Aix Marseille Université, Université de Toulon, CNRS UMR 7020, LISMarseilleFrance

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