Cross Tensor Approximation Methods for Compression and Dimensionality Reduction

Cross Tensor Approximation (CTA) is a generalization of Cross/skeleton matrix and CUR Matrix Approximation (CMA) and is a suitable tool for fast low-rank tensor approximation. It facilitates interpreting the underlying data tensors and decomposing/compressing tensors so that their structures, such a...

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Autores principales:	Salman Ahmadi-Asl, Cesar F. Caiafa, Andrzej Cichocki, Anh Huy Phan, Toshihisa Tanaka, Ivan Oseledets, Jun Wang
Formato:	article
Lenguaje:	EN
Publicado:	IEEE 2021
Materias:	CUR algorithms cross approximation tensor decomposition tubal SVD randomization Electrical engineering. Electronics. Nuclear engineering TK1-9971
Acceso en línea:	https://doaj.org/article/27dcdaa27af141ec971b8decec419b56
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spelling	oai:doaj.org-article:27dcdaa27af141ec971b8decec419b562021-11-18T00:08:43ZCross Tensor Approximation Methods for Compression and Dimensionality Reduction2169-353610.1109/ACCESS.2021.3125069https://doaj.org/article/27dcdaa27af141ec971b8decec419b562021-01-01T00:00:00Zhttps://ieeexplore.ieee.org/document/9599673/https://doaj.org/toc/2169-3536Cross Tensor Approximation (CTA) is a generalization of Cross/skeleton matrix and CUR Matrix Approximation (CMA) and is a suitable tool for fast low-rank tensor approximation. It facilitates interpreting the underlying data tensors and decomposing/compressing tensors so that their structures, such as nonnegativity, smoothness, or sparsity, can be potentially preserved. This paper reviews and extends state-of-the-art deterministic and randomized algorithms for CTA with intuitive graphical illustrations. We discuss several possible generalizations of the CMA to tensors, including CTAs: based on fiber selection, slice-tube selection, and lateral-horizontal slice selection. The main focus is on the CTA algorithms using Tucker and tubal SVD (t-SVD) models while we provide references to other decompositions such as Tensor Train (TT), Hierarchical Tucker (HT), and Canonical Polyadic (CP) decompositions. We evaluate the performance of the CTA algorithms by extensive computer simulations to compress color and medical images and compare their performance.Salman Ahmadi-AslCesar F. CaiafaAndrzej CichockiAnh Huy PhanToshihisa TanakaIvan OseledetsJun WangIEEEarticleCUR algorithmscross approximationtensor decompositiontubal SVDrandomizationElectrical engineering. Electronics. Nuclear engineeringTK1-9971ENIEEE Access, Vol 9, Pp 150809-150838 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	CUR algorithms cross approximation tensor decomposition tubal SVD randomization Electrical engineering. Electronics. Nuclear engineering TK1-9971
spellingShingle	CUR algorithms cross approximation tensor decomposition tubal SVD randomization Electrical engineering. Electronics. Nuclear engineering TK1-9971 Salman Ahmadi-Asl Cesar F. Caiafa Andrzej Cichocki Anh Huy Phan Toshihisa Tanaka Ivan Oseledets Jun Wang Cross Tensor Approximation Methods for Compression and Dimensionality Reduction
description	Cross Tensor Approximation (CTA) is a generalization of Cross/skeleton matrix and CUR Matrix Approximation (CMA) and is a suitable tool for fast low-rank tensor approximation. It facilitates interpreting the underlying data tensors and decomposing/compressing tensors so that their structures, such as nonnegativity, smoothness, or sparsity, can be potentially preserved. This paper reviews and extends state-of-the-art deterministic and randomized algorithms for CTA with intuitive graphical illustrations. We discuss several possible generalizations of the CMA to tensors, including CTAs: based on fiber selection, slice-tube selection, and lateral-horizontal slice selection. The main focus is on the CTA algorithms using Tucker and tubal SVD (t-SVD) models while we provide references to other decompositions such as Tensor Train (TT), Hierarchical Tucker (HT), and Canonical Polyadic (CP) decompositions. We evaluate the performance of the CTA algorithms by extensive computer simulations to compress color and medical images and compare their performance.
format	article
author	Salman Ahmadi-Asl Cesar F. Caiafa Andrzej Cichocki Anh Huy Phan Toshihisa Tanaka Ivan Oseledets Jun Wang
author_facet	Salman Ahmadi-Asl Cesar F. Caiafa Andrzej Cichocki Anh Huy Phan Toshihisa Tanaka Ivan Oseledets Jun Wang
author_sort	Salman Ahmadi-Asl
title	Cross Tensor Approximation Methods for Compression and Dimensionality Reduction
title_short	Cross Tensor Approximation Methods for Compression and Dimensionality Reduction
title_full	Cross Tensor Approximation Methods for Compression and Dimensionality Reduction
title_fullStr	Cross Tensor Approximation Methods for Compression and Dimensionality Reduction
title_full_unstemmed	Cross Tensor Approximation Methods for Compression and Dimensionality Reduction
title_sort	cross tensor approximation methods for compression and dimensionality reduction
publisher	IEEE
publishDate	2021
url	https://doaj.org/article/27dcdaa27af141ec971b8decec419b56
work_keys_str_mv	AT salmanahmadiasl crosstensorapproximationmethodsforcompressionanddimensionalityreduction AT cesarfcaiafa crosstensorapproximationmethodsforcompressionanddimensionalityreduction AT andrzejcichocki crosstensorapproximationmethodsforcompressionanddimensionalityreduction AT anhhuyphan crosstensorapproximationmethodsforcompressionanddimensionalityreduction AT toshihisatanaka crosstensorapproximationmethodsforcompressionanddimensionalityreduction AT ivanoseledets crosstensorapproximationmethodsforcompressionanddimensionalityreduction AT junwang crosstensorapproximationmethodsforcompressionanddimensionalityreduction
_version_	1718425212783951872

Cross Tensor Approximation Methods for Compression and Dimensionality Reduction

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