High-Dimensional Data Learning Based on Tensorial-Singular Space of Tensor Train Cores

Ouafae, Karmouda; Boyer, Remy; Jeremie, Boulanger

Document type :

Autre communication scientifique (congrès sans actes - poster - séminaire...): Communication dans un congrès avec actes

Title :

High-Dimensional Data Learning Based on Tensorial-Singular Space of Tensor Train Cores

Author(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]

Conference title :

EUSIPCO

City :

Belgrade

Start date of the conference :

2022-08-29

English keyword(s) :

Tensor Train Decomposition
subspaces
kernel

HAL domain(s) :

Sciences de l'ingénieur [physics]/Traitement du signal et de l'image [eess.SP]
Mathématiques [math]

English abstract : [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. ...
Show more >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.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL

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https://hal.univ-lille.fr/hal-03672088/document
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