دورية أكاديمية
Computing the polyadic decomposition of nonnegative third order tensors
| العنوان: | Computing the polyadic decomposition of nonnegative third order tensors |
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| المؤلفون: | Royer, Jean-Philip, Thirion-Moreau, Nadège, Comon, Pierre |
| المساهمون: | Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe SIGNAL, Signal, Images et Systèmes (Laboratoire I3S - SIS), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), Université Nice Sophia Antipolis (1965 - 2019) (UNS)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UniCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UniCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), Université Nice Sophia Antipolis (1965 - 2019) (UNS)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UniCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UniCA), Laboratoire de sondages électromagnétiques de l'environnement terrestre (LSEET), Institut national des sciences de l'Univers (INSU - CNRS)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon) (LIS), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Signal et Image (SIIM), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Université de Toulon - École d’ingénieurs SeaTech (UTLN SeaTech), Université de Toulon (UTLN), PRES euro-m{é}diterran{é}en |
| المصدر: | ISSN: 0165-1684. |
| بيانات النشر: | HAL CCSD Elsevier |
| سنة النشر: | 2011 |
| المجموعة: | HAL Université Côte d'Azur |
| مصطلحات موضوعية: | Data analysis, Nonlinear conjugate gradient, preconditioning, Quasi-Newton, BFGS, DFP, nonnegative, 3-way, array, tensor, factorization, multi-way, Canonical Polyadic decomposition, CP decomposition, Canonical decomposition, CanDecomp, Parafac, Chemometrics, Data mining, Fluorescence, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing |
| الوصف: | International audience ; Computing the minimal polyadic decomposition (also often referred to as canonical decomposition, or sometimes Parafac) amounts to finding the global minimum of a coercive polynomial in many variables. In the case of arrays with nonnegative entries, the low-rank approximation problem is well posed. In addition, due to the large dimension of the problem, the decomposition can be rather efficiently calculated with the help of preconditioned nonlinear conjugate gradient algorithms, as subsequently shown, if equipped with an algebraic calculation of the globally optimal stepsize in low dimension. Other algorithms are also studied (gradient and quasi-Newton approaches) for comparisons. Two versions of each algorithm are considered: the Enhanced Line Search version (ELS), and the backtracking version alternating with ELS. Computer simulations are provided and demonstrate the good behavior of these algorithms dedicated to nonnegative arrays, compared to others put forward in the literature. Finally, applications in the context of data analysis illustrate various algorithms. The main advantage of the suggested approach is to explicitly take into account the nonnegative nature of the loading matrices in the problem parameterization, instead of enforcing positive entries by projection. According to the experiments we have run, such an approach also happens to be more robust with respect to possible modeling errors. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| العلاقة: | hal-00618729; https://hal.science/hal-00618729Test; https://hal.science/hal-00618729/documentTest; https://hal.science/hal-00618729/file/artRTC-v13.pdfTest |
| DOI: | 10.1016/j.sigpro.2011.03.006 |
| الإتاحة: | https://doi.org/10.1016/j.sigpro.2011.03.006Test https://hal.science/hal-00618729Test https://hal.science/hal-00618729/documentTest https://hal.science/hal-00618729/file/artRTC-v13.pdfTest |
| حقوق: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.798141BA |
| قاعدة البيانات: | BASE |
| DOI: | 10.1016/j.sigpro.2011.03.006 |
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