Skip to Main content Skip to Navigation
Conference papers

Fast multilinear Singular Values Decomposition for higher-order Hankel tensors

Abstract : The Higher-Order Singular Value Decomposition (HOSVD) is a possible generalization of the Singular Value Decomposition (SVD) to tensors, which have been successfully applied in various domains. Unfortunately, this decomposition is computationally demanding. Indeed, the HOSVD of a Nth- order tensor involves the computation of the SVD of N matrices. Previous works have shown that it is possible to reduce the complexity of HOSVD for third-order structured tensors. These methods exploit the columns redundancy, which is present in the mode of structured tensors, especially in Hankel tensors. In this paper, we propose to extend these results to fourth order Hankel tensor. We propose two ways to extend Hankel structure to fourth order tensors. For these two types of tensors, a method to build a reordered mode is proposed, which highlights the column redundancy and we derive a fast algorithm to compute their HOSVD. Finally we show the benefit of our algorithms in terms of complexity.
Document type :
Conference papers
Complete list of metadatas

Cited literature [16 references]  Display  Hide  Download

https://hal-supelec.archives-ouvertes.fr/hal-01005002
Contributor : Remy Boyer <>
Submitted on : Wednesday, June 11, 2014 - 7:10:57 PM
Last modification on : Monday, October 12, 2020 - 10:30:32 AM
Long-term archiving on: : Thursday, September 11, 2014 - 12:55:39 PM

File

1569922753_3_.pdf
Files produced by the author(s)

Licence


Distributed under a Creative Commons Attribution - NonCommercial - ShareAlike 4.0 International License

Identifiers

  • HAL Id : hal-01005002, version 1

Citation

Maxime Boizard, Remy Boyer, Gérard Favier, Pascal Larzabal. Fast multilinear Singular Values Decomposition for higher-order Hankel tensors. IEEE Sensor Array and Multichannel Signal Processing Workshop - Invited article, Jun 2014, A Coruña, Spain. 4 p. ⟨hal-01005002⟩

Share

Metrics

Record views

1070

Files downloads

540