High-Dimensional Data Learning Based on ...
Type de document :
Autre communication scientifique (congrès sans actes - poster - séminaire...): Communication dans un congrès avec actes
Titre :
High-Dimensional Data Learning Based on Tensorial-Singular Space of Tensor Train Cores
Auteur(s) :
Ouafae, Karmouda [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Boyer, Remy [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Jeremie, Boulanger [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Boyer, Remy [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Jeremie, Boulanger [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Titre de la manifestation scientifique :
EUSIPCO
Ville :
Belgrade
Date de début de la manifestation scientifique :
2022-08-29
Mot(s)-clé(s) en anglais :
Tensor Train Decomposition
subspaces
kernel
subspaces
kernel
Discipline(s) HAL :
Sciences de l'ingénieur [physics]/Traitement du signal et de l'image [eess.SP]
Mathématiques [math]
Mathématiques [math]
Résumé en anglais : [en]
Tensors are multidimensional data structures used to represent many real world data. In the context of supervised learning, Support Vector Machines (SVMs) are known to be very efficient for different classification tasks. ...
Lire la suite >Tensors are multidimensional data structures used to represent many real world data. In the context of supervised learning, Support Vector Machines (SVMs) are known to be very efficient for different classification tasks. In this work, we propose a kernel metric for SVM to deal with non linear classification problems. First, we use the Tensor Train Decomposition (TTD) to decompose a tensor into TT-cores of order three and two matrices. In order to mitigate the problem of non-uniqueness of TTD, we propose a kernel based on the tensorial singular subspaces spanned by TT-cores. The TT-based kernel function proposed is based on the tools of t-Algebra of 3-rd order tensors. We also show that it is possible to use different kernel functions on each TT-core. Numerical experiments on real-world datasets show the competitivity of our approach compared to existing methods and the superiority of our method when dealing with few-sample of high-dimensional inputs.Lire moins >
Lire la suite >Tensors are multidimensional data structures used to represent many real world data. In the context of supervised learning, Support Vector Machines (SVMs) are known to be very efficient for different classification tasks. In this work, we propose a kernel metric for SVM to deal with non linear classification problems. First, we use the Tensor Train Decomposition (TTD) to decompose a tensor into TT-cores of order three and two matrices. In order to mitigate the problem of non-uniqueness of TTD, we propose a kernel based on the tensorial singular subspaces spanned by TT-cores. The TT-based kernel function proposed is based on the tools of t-Algebra of 3-rd order tensors. We also show that it is possible to use different kernel functions on each TT-core. Numerical experiments on real-world datasets show the competitivity of our approach compared to existing methods and the superiority of our method when dealing with few-sample of high-dimensional inputs.Lire moins >
Langue :
Anglais
Comité de lecture :
Oui
Audience :
Internationale
Vulgarisation :
Non
Collections :
Source :
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- 20220225021507_979369_1291.pdf
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