NonNegative 3-Way tensor Factorzation taking into account Possible Missing Data

Jean-Philip Royer 1 Nadège Thirion-Moreau 2, 3, 4 Pierre Comon 5, *
* Corresponding author
1 SIGNAL
LSIS - Laboratoire des Sciences de l'Information et des Systèmes
2 LIS - Laboratoire Interfaces Sensorielles
DIASI - Département Intelligence Ambiante et Systèmes Interactifs : DRT/LIST/DIASI
3 SIIM - Signal et Image
LIS - Laboratoire d'Informatique et Systèmes
5 GIPSA-CICS - CICS
GIPSA-DIS - Département Images et Signal
Abstract : The paper deals with the problem of incomplete data i.e. data with missing, unknown or unreliable values, in the polyadic decomposition of a nonnegative three-way tensor. The main advantage of the nonnegativity constraint is that the approximation problem becomes well posed. To tackle simultaneously these two problems, we suggest the use of a weighted least square cost function whose weights are gradually modified through the iterations. Moreover, the nonnegative nature of the loading matrices is taken into account directly in the problem parameterization. Then, the three gradient components can be explicitly derived allowing to efficiently implement the CP decomposition using standard optimization algorithms. In our case, we focus on the conjugate gradient and the BFGS algorithms. Finally, the good behavior of the proposed approaches and their robustness versus possible model errors is illustrated through computer simulations in the context of data analysis.
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Jean-Philip Royer, Nadège Thirion-Moreau, Pierre Comon. NonNegative 3-Way tensor Factorzation taking into account Possible Missing Data. 20th European Signal Processing Conference (EUSIPCO-2012), Aug 2012, Bucarest, Romania. pp.1-5. ⟨hal-00725289⟩

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