On tensor tubal-Krylov subspace methods

Ichi, Alaa El; Jbilou, Khalide; Sadaka, Rachid

doi:10.1080/03081087.2021.1999381

Cited by 10 publications

(7 citation statements)

References 14 publications

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“…Then, we have the following results [17] PROPOSITION 4.1. The tensors produced by the tensor c-global Golub-Kahan algorithm satisfy the following relations…”

Section: Compute the Euclidean Distancementioning

confidence: 86%

“…Due to the increasing volume of data required by these applications, approximative low-rank matrix and tensor factorizations play a fundamental role in extracting latent components. The idea is to replace the initial large and maybe noisy and ill conditioned large scale original data by a lower dimensional approximate representation obtained via a matrix or multi-way array factorization or decomposition; see [1,2,4,13,14,16,17,18,15,20] for more details on recent work related to tensors and applications. In the present work, we consider third order tensors that could be defined as three dimensional arrays of data.…”

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confidence: 99%

“…[17] Let a ∈ R 1×1×n 3 and B ∈ R n 1 ×n 2 ×n 3 , the tube fiber tensor product(a B) is an (n 1 × n 2 × n 3 )tensor defined by a B =    a c b(1, 1, :) . .…”

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confidence: 99%

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A multidimensional principal component analysis via the c-product Golub-Kahan-SVD for classification and face recognition

Hached¹,

Jbilou²,

Koukouvinos³

et al. 2021

Preprint

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Face recognition and identification is a very important application in machine learning. Due to the increasing amount of available data, traditional approaches based on matricization and matrix PCA methods can be difficult to implement. Moreover, the tensorial approaches are a natural choice, due to the mere structure of the databases, for example in the case of color images. Nevertheless, even though various authors proposed factorization strategies for tensors, the size of the considered tensors can pose some serious issues. When only a few features are needed to construct the projection space, there is no need to compute a SVD on the whole data. Two versions of the tensor Golub-Kahan algorithm are considered in this manuscript, as an alternative to the classical use of the tensor SVD which is based on truncated strategies. In this paper, we consider the Tensor Tubal Golub Kahan Principal Component Analysis method which purpose it to extract the main features of images using the tensor singular value decomposition (SVD) based on the tensor cosine product that uses the discrete cosine transform. This approach is applied for classification and face recognition and numerical tests show its effectiveness.

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“…Then, we have the following results [17] PROPOSITION 4.1. The tensors produced by the tensor c-global Golub-Kahan algorithm satisfy the following relations…”

Section: Compute the Euclidean Distancementioning

confidence: 86%

mentioning

confidence: 99%

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A multidimensional principal component analysis via the c-product Golub-Kahan-SVD for classification and face recognition

Hached¹,

Jbilou²,

Koukouvinos³

et al. 2021

Preprint

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“…Recently, the tensor T-product has been proved to be a useful tool in many real applications [1,2,7,8,6,5,13,21,18,23,24,28,29,30,31,32,33,34,37,46,48]. Wang et al [40] investigate the tensor neural network models based on the tensor singular value decomposition (T-SVD).…”

Section: Introductionmentioning

confidence: 99%

Tensor LU and QR decompositions and their randomized algorithms

Zhu

Wei

2022

CMCMA

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In this paper, we propose two decompositions extended from matrices to tensors, including LU and QR decompositions with their rank-revealing and randomized variations. We give the growth order analysis of error of the tensor QR (t-QR) and tensor LU (t-LU) decompositions. Growth order of error and running time are shown by numerical examples. We test our methods by compressing and analyzing the imagebased data, showing that the performance of tensor randomized QR decomposition is better than the tensor randomized SVD (t-rSVD) in terms of the accuracy, running time and memory.

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“…The CP and the Tucker compressions were introduced as natural generalization of the classical singular value decomposition (SVD) for matrices; see [15,4,12,13,24]. In the last years, new tensor-tensor products such as cosine-product (c-product), using discrete cosine or T-product, using Fast Fourier Transform (FFT), were introduced for third-order tensors, studied and applied to image processing and other fields; see [19,1,25,13,20]. In the present paper, we generalize those tensor-tensor products for high-order tensors.…”

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confidence: 99%

Generalized L-product for hight order tensors with applications using GPU computation

Tbib¹,

Elalj²,

Hachimi³

et al. 2022

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In this paper, we will present a generalization of the L-tensor product ( * L -product) including generalization of the well known tensor cosine and T-products that were defined for third-order tensors and based on fast Fourier transform and discrete cosine transform (DCT). We will give some applications on tensor completion. To solve some optimization problems linked with the problem of tensor completion, we will use the Proximal Gradient Algorithm (PGA) to solve some derived optimization problems. Numerical tests are given to show the effectiveness of the proposed methods and also present some tests using GPU computation.

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On tensor tubal-Krylov subspace methods

Cited by 10 publications

References 14 publications

A multidimensional principal component analysis via the c-product Golub-Kahan-SVD for classification and face recognition

A multidimensional principal component analysis via the c-product Golub-Kahan-SVD for classification and face recognition

Tensor LU and QR decompositions and their randomized algorithms

Generalized L-product for hight order tensors with applications using GPU computation

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