Tucker Decomposition Based on a Tensor ...
Document type :
Pré-publication ou Document de travail
Title :
Tucker Decomposition Based on a Tensor Train of Coupled and Constrained CP Cores
Author(s) :
Giraud, Maxence [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Itier, Vincent [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Ecole nationale supérieure Mines-Télécom Lille Douai [IMT Nord Europe]
Boyer, Remy [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Zniyed, Yassine [Auteur]
Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon) [LIS]
de Almeida, André [Auteur]
Wireless Telecom Research Group [Fortaleza] [GTEL]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Itier, Vincent [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Ecole nationale supérieure Mines-Télécom Lille Douai [IMT Nord Europe]
Boyer, Remy [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Zniyed, Yassine [Auteur]
Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon) [LIS]
de Almeida, André [Auteur]
Wireless Telecom Research Group [Fortaleza] [GTEL]
Publication date :
2023
English keyword(s) :
Tensor
Tucker decomposition
Constrained CPD
Tensor Train
Multilinear Algebra
Tucker decomposition
Constrained CPD
Tensor Train
Multilinear Algebra
HAL domain(s) :
Sciences de l'ingénieur [physics]/Traitement du signal et de l'image [eess.SP]
English abstract : [en]
Many real-life signal-based applications use the Tucker decomposition of a high dimensional/order tensor. A well-known problem with the Tucker model is that its number of entries increases exponentially with its order, a ...
Show more >Many real-life signal-based applications use the Tucker decomposition of a high dimensional/order tensor. A well-known problem with the Tucker model is that its number of entries increases exponentially with its order, a phenomenon known as the "curse of the dimensionality". The Higher-Order Orthogonal Iteration (HOOI) and Higher-Order Singular Value Decomposition (HOSVD) are known as the gold standard for computing the range span of the factor matrices of a Tucker Decomposition but also suffer from the curse. In this paper, we propose a new methodology with a similar estimation accuracy as the HOSVD with non-exploding computational and storage costs. If the noise-free data follows a Tucker decomposition, the corresponding Tensor Train (TT) decomposition takes a remarkable specific structure. More precisely, we prove that for a Q-order Tucker tensor, the corresponding TT decomposition is constituted by Q − 3 3-order TT-core tensors that follow a Constrained Canonical Polyadic Decomposition. Using this new formulation and the coupling property between neighboring TTcores, we propose a JIRAFE-type scheme for the Tucker decomposition, called TRIDENT. Our numerical simulations show that the proposed method offers a drastically reduced complexity compared to the HOSVD and HOOI while outperforming the Fast Multilinear Projection (FMP) method in terms of estimation accuracy.Show less >
Show more >Many real-life signal-based applications use the Tucker decomposition of a high dimensional/order tensor. A well-known problem with the Tucker model is that its number of entries increases exponentially with its order, a phenomenon known as the "curse of the dimensionality". The Higher-Order Orthogonal Iteration (HOOI) and Higher-Order Singular Value Decomposition (HOSVD) are known as the gold standard for computing the range span of the factor matrices of a Tucker Decomposition but also suffer from the curse. In this paper, we propose a new methodology with a similar estimation accuracy as the HOSVD with non-exploding computational and storage costs. If the noise-free data follows a Tucker decomposition, the corresponding Tensor Train (TT) decomposition takes a remarkable specific structure. More precisely, we prove that for a Q-order Tucker tensor, the corresponding TT decomposition is constituted by Q − 3 3-order TT-core tensors that follow a Constrained Canonical Polyadic Decomposition. Using this new formulation and the coupling property between neighboring TTcores, we propose a JIRAFE-type scheme for the Tucker decomposition, called TRIDENT. Our numerical simulations show that the proposed method offers a drastically reduced complexity compared to the HOSVD and HOOI while outperforming the Fast Multilinear Projection (FMP) method in terms of estimation accuracy.Show less >
Language :
Anglais
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