Nonnegative Structured Kruskal Tensor Regression

Xinjue Wang; Esa Ollila; Sergiy A. Vorobyov

doi:10.1109/CAMSAP58249.2023.10403474

Nonnegative Structured Kruskal Tensor Regression

Xinjue Wang, Esa Ollila, Sergiy A. Vorobyov

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

17 Downloads (Pure)

Abstract

Many contemporary data analysis problems use tensors (multidimensional arrays) as covariates. For example, regression or classification tasks may need to be performed on a set of image covariates sampled from diffusion tensor imaging (DTI), functional magnetic resonance imaging (fMRI), or hyperspectral imaging (HSI). By en-forcing a low-rank constraint on the parameter tensor, tensor regression models effectively leverage the temporal and spatial structure of tensor covariates. In this paper, we study Kruskal tensor regression with sparsity and smoothness inducing regularization and non-negativity constraints. We solve the corresponding penalized nonnegative Kruskal tensor regression (KTR) problem using an efficient block-wise alternating minimization method. The efficiency of the proposed approach is illustrated via simulations.

Original language	English
Title of host publication	2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2023
Publisher	IEEE
Pages	441-445
Number of pages	5
ISBN (Electronic)	979-8-3503-4452-3
DOIs	https://doi.org/10.1109/CAMSAP58249.2023.10403474
Publication status	Published - 2023
MoE publication type	A4 Conference publication
Event	IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing - Herradura, Costa Rica Duration: 10 Dec 2023 → 13 Dec 2023 Conference number: 9

Publication series

Name	2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2023

Workshop

Workshop	IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing
Abbreviated title	CAMSAP
Country/Territory	Costa Rica
City	Herradura
Period	10/12/2023 → 13/12/2023

Keywords

fused LASSO
Kruskal tensor
PARAFAC
Sparsity
tensor regression

Access to Document

10.1109/CAMSAP58249.2023.10403474

CAMSAP23_Nonnegative_Structured_Kruskal_Tensor_RegressionAccepted author manuscript, 432 KB

Cite this

Wang, X., Ollila, E., & Vorobyov, S. A. (2023). Nonnegative Structured Kruskal Tensor Regression. In 2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2023 (pp. 441-445). (2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2023). IEEE. https://doi.org/10.1109/CAMSAP58249.2023.10403474

@inproceedings{9f8acb8ec874456aa99537dfbd2773f7,

title = "Nonnegative Structured Kruskal Tensor Regression",

abstract = "Many contemporary data analysis problems use tensors (multidimensional arrays) as covariates. For example, regression or classification tasks may need to be performed on a set of image covariates sampled from diffusion tensor imaging (DTI), functional magnetic resonance imaging (fMRI), or hyperspectral imaging (HSI). By en-forcing a low-rank constraint on the parameter tensor, tensor regression models effectively leverage the temporal and spatial structure of tensor covariates. In this paper, we study Kruskal tensor regression with sparsity and smoothness inducing regularization and non-negativity constraints. We solve the corresponding penalized nonnegative Kruskal tensor regression (KTR) problem using an efficient block-wise alternating minimization method. The efficiency of the proposed approach is illustrated via simulations.",

keywords = "fused LASSO, Kruskal tensor, PARAFAC, Sparsity, tensor regression",

author = "Xinjue Wang and Esa Ollila and Vorobyov, {Sergiy A.}",

note = "Publisher Copyright: {\textcopyright} 2023 IEEE.; IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP ; Conference date: 10-12-2023 Through 13-12-2023",

year = "2023",

doi = "10.1109/CAMSAP58249.2023.10403474",

language = "English",

series = "2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2023",

publisher = "IEEE",

pages = "441--445",

booktitle = "2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2023",

address = "United States",

}

Wang, X , Ollila, E & Vorobyov, SA 2023, Nonnegative Structured Kruskal Tensor Regression. in 2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2023. 2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2023, IEEE, pp. 441-445, IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, Herradura, Costa Rica, 10/12/2023. https://doi.org/10.1109/CAMSAP58249.2023.10403474

Nonnegative Structured Kruskal Tensor Regression. / Wang, Xinjue ; Ollila, Esa ; Vorobyov, Sergiy A.
2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2023. IEEE, 2023. p. 441-445 (2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2023).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

TY - GEN

T1 - Nonnegative Structured Kruskal Tensor Regression

AU - Wang, Xinjue

AU - Ollila, Esa

AU - Vorobyov, Sergiy A.

N1 - Conference code: 9

PY - 2023

Y1 - 2023

N2 - Many contemporary data analysis problems use tensors (multidimensional arrays) as covariates. For example, regression or classification tasks may need to be performed on a set of image covariates sampled from diffusion tensor imaging (DTI), functional magnetic resonance imaging (fMRI), or hyperspectral imaging (HSI). By en-forcing a low-rank constraint on the parameter tensor, tensor regression models effectively leverage the temporal and spatial structure of tensor covariates. In this paper, we study Kruskal tensor regression with sparsity and smoothness inducing regularization and non-negativity constraints. We solve the corresponding penalized nonnegative Kruskal tensor regression (KTR) problem using an efficient block-wise alternating minimization method. The efficiency of the proposed approach is illustrated via simulations.

AB - Many contemporary data analysis problems use tensors (multidimensional arrays) as covariates. For example, regression or classification tasks may need to be performed on a set of image covariates sampled from diffusion tensor imaging (DTI), functional magnetic resonance imaging (fMRI), or hyperspectral imaging (HSI). By en-forcing a low-rank constraint on the parameter tensor, tensor regression models effectively leverage the temporal and spatial structure of tensor covariates. In this paper, we study Kruskal tensor regression with sparsity and smoothness inducing regularization and non-negativity constraints. We solve the corresponding penalized nonnegative Kruskal tensor regression (KTR) problem using an efficient block-wise alternating minimization method. The efficiency of the proposed approach is illustrated via simulations.

KW - fused LASSO

KW - Kruskal tensor

KW - PARAFAC

KW - Sparsity

KW - tensor regression

UR - http://www.scopus.com/inward/record.url?scp=85185007454&partnerID=8YFLogxK

U2 - 10.1109/CAMSAP58249.2023.10403474

DO - 10.1109/CAMSAP58249.2023.10403474

M3 - Conference article in proceedings

AN - SCOPUS:85185007454

T3 - 2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2023

SP - 441

EP - 445

BT - 2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2023

PB - IEEE

T2 - IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing

Y2 - 10 December 2023 through 13 December 2023

ER -

Wang X , Ollila E , Vorobyov SA. Nonnegative Structured Kruskal Tensor Regression. In 2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2023. IEEE. 2023. p. 441-445. (2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2023). doi: 10.1109/CAMSAP58249.2023.10403474

Nonnegative Structured Kruskal Tensor Regression

Abstract

Publication series

Workshop

Keywords

Access to Document

Other files and links

Fingerprint

Cite this