Structured Tensor-Train Decomposition for Speeding-Up Kernel-Based Learning

Yassine Zniyed; Ouafae Karmouda; Jérémie Boulanger; Remy Boyer; André L. F. de Almeida; Gérard Favier

Chapitre d'ouvrage

Structured Tensor-Train Decomposition for Speeding-Up Kernel-Based Learning

Yassine Zniyed ¹ Ouafae Karmouda ^{2, 3} Jérémie Boulanger ^{2, 3} Remy Boyer ^{2, 3} André L. F. de Almeida ⁴ Gérard Favier ⁵

1 CRAN - Centre de Recherche en Automatique de Nancy

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

3 University of Lille

4 GTEL - Wireless Telecom Research Group [Fortaleza]

5 I3S - Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis

Abstract : In this chapter, we present an algebraic relation between the Tucker model and the Tensor-Train decomposition with structured cores. Exploiting this link, we present a new fastalgorithm to compute the dominant singular subspaces of a푄-order tensor. As opposedto the state of the art methods (usually called HOSVD for high-order SVD), our approachmitigates the well-known “curse of dimentionality”. This approach is applied to speedup kernel-based supervised tensor classification.

Keywords : Structured Tensors Tucker decomposition Tensor Trains HOSVD Classification

Type de document :

Chapitre d'ouvrage

Domaine :

Mathématiques [math]

Sciences de l'ingénieur [physics]

Liste complète des métadonnées

https://hal.univ-lille.fr/hal-03264296
Contributeur : Remy Boyer <>
Soumis le : vendredi 18 juin 2021 - 09:42:16
Dernière modification le : mardi 22 juin 2021 - 18:19:03

Structured Tensor-Train Decomposition for Speeding-Up Kernel-Based Learning

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Structured Tensor-Train Decomposition for Speeding-Up Kernel-Based Learning

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