A TT-Based Hierarchical Framework for ...
Document type :
Compte-rendu et recension critique d'ouvrage
DOI :
Title :
A TT-Based Hierarchical Framework for Decomposing High-Order Tensors
Author(s) :
Zniyed, Yassine [Auteur]
Laboratoire des signaux et systèmes [L2S]
Boyer, Remy [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
de Almeida, André [Auteur]
Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe SIGNAL
Favier, Gérard [Auteur]
Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe SIGNAL
Laboratoire des signaux et systèmes [L2S]
Boyer, Remy [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
de Almeida, André [Auteur]
Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe SIGNAL
Favier, Gérard [Auteur]
Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe SIGNAL
Journal title :
SIAM Journal on Scientific Computing
Pages :
A822-A848
Publisher :
Society for Industrial and Applied Mathematics
Publication date :
2020-01
ISSN :
1064-8275
English keyword(s) :
Tensor Train
hierarchical SVD
dimensionality reduction
tensor graph
hierarchical SVD
dimensionality reduction
tensor graph
HAL domain(s) :
Mathématiques [math]
Sciences de l'ingénieur [physics]/Traitement du signal et de l'image [eess.SP]
Sciences de l'ingénieur [physics]/Traitement du signal et de l'image [eess.SP]
English abstract : [en]
In the context of big data, high-order tensor decompositions have to face a new challenge in terms of storage and computational costs. The tensor train (TT) decomposition provides a very useful graph-based model reduction, ...
Show more >In the context of big data, high-order tensor decompositions have to face a new challenge in terms of storage and computational costs. The tensor train (TT) decomposition provides a very useful graph-based model reduction, whose storage cost grows linearly with the tensor order D. The computation of the TT-core tensors and TT-ranks can be done in a stable sequential (i.e., non-iterative) way thanks to the popular TT-SVD algorithm. In this paper, we exploit the ideas developed for the hierarchical/tree Tucker decomposition in the context of the TT decomposition. Specifically, a new efficient estimation scheme, called TT-HSVD for Tensor-Train Hierarchical SVD, is proposed as a solution to compute the TT decomposition of a high-order tensor. The new algorithm simultaneously delivers the TT-core tensors and their TT-ranks in a hierarchical way. It is a stable (i.e., non-iterative) and computationally more efficient algorithm than the TT-SVD one, which is very important when dealing with large-scale data. The TT-HSVD algorithm uses a new reshaping strategy and a tailored partial SVD, which allows to deal with smaller matrices compared to those of the TT-SVD. In addition, TT-HSVD suits well for a parallel processing architecture. An algebraic analysis of the two algorithms is carried out, showing that TT-SVD and TT-HSVD compute the same TT-ranks and TT-core tensors up to specific bases. Simulation results for different tensor orders and dimensions corroborate the effectiveness of the proposed algorithm.Show less >
Show more >In the context of big data, high-order tensor decompositions have to face a new challenge in terms of storage and computational costs. The tensor train (TT) decomposition provides a very useful graph-based model reduction, whose storage cost grows linearly with the tensor order D. The computation of the TT-core tensors and TT-ranks can be done in a stable sequential (i.e., non-iterative) way thanks to the popular TT-SVD algorithm. In this paper, we exploit the ideas developed for the hierarchical/tree Tucker decomposition in the context of the TT decomposition. Specifically, a new efficient estimation scheme, called TT-HSVD for Tensor-Train Hierarchical SVD, is proposed as a solution to compute the TT decomposition of a high-order tensor. The new algorithm simultaneously delivers the TT-core tensors and their TT-ranks in a hierarchical way. It is a stable (i.e., non-iterative) and computationally more efficient algorithm than the TT-SVD one, which is very important when dealing with large-scale data. The TT-HSVD algorithm uses a new reshaping strategy and a tailored partial SVD, which allows to deal with smaller matrices compared to those of the TT-SVD. In addition, TT-HSVD suits well for a parallel processing architecture. An algebraic analysis of the two algorithms is carried out, showing that TT-SVD and TT-HSVD compute the same TT-ranks and TT-core tensors up to specific bases. Simulation results for different tensor orders and dimensions corroborate the effectiveness of the proposed algorithm.Show less >
Language :
Anglais
Popular science :
Non
Collections :
Source :
Files
- https://hal.archives-ouvertes.fr/hal-02436368/document
- Open access
- Access the document
- https://hal.archives-ouvertes.fr/hal-02436368/document
- Open access
- Access the document
- https://hal.archives-ouvertes.fr/hal-02436368/document
- Open access
- Access the document
- document
- Open access
- Access the document
- TT_HSVD_SIAM.pdf
- Open access
- Access the document
- TT_HSVD_SIAM.pdf
- Open access
- Access the document