Extension of the semi-algebraic framework for approximate CP decompositions via simultaneous matrix diagonalization to the efficient calculation of coupled CP decompositions

Naskovska, Kristina; Haardt, Martin

doi:10.1109/acssc.2016.7869678

Cited by 11 publications

(15 citation statements)

References 11 publications

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“…(1) and X (2) have the factor matrix A in common, the unitary matrix U 1 should be the same for both HOSVDs. The C-SECSI framework provides an efficient computation of the coupled CP decomposition using the joint HOSVD followed by the whole set of possible SMDs [2].…”

Section: Tensor Algebra and Coupled Cp Decompositionmentioning

confidence: 99%

Section: Tensor Algebra and Coupled Cp Decompositionmentioning

confidence: 99%

“…The C-SECSI framework provides an efficient computation of the coupled CP decomposition using the joint HOSVD followed by the whole set of possible SMDs [2]. Eight initial estimates of the factor matrices are obtained, if the two tensors have one factor matrix in common, as shown in [2]. All estimates of the factor matrices, as well as an indication whether they are estimated from a transform matrix, from the diagonalized tensor, estimated via LS (Least Squeares) or a joint LS fit are summarized in Table I.…”

Section: Tensor Algebra and Coupled Cp Decompositionmentioning

confidence: 99%

“…The coupled CP decomposition jointly decomposes tensors that have at least one factor matrix in common. A C-SECSI framework for the efficient computation of the coupled CP decomposition was proposed in [2]. The C-SECSI framework is an extension of the SECSI framework [3], [4] for the robust estimation of coupled CP decompositions based on a truncated joint HOSVD (Higher Order Singular Value Decomposition) followed by the whole set of possible SMDs (Simultaneous Matrix Diagonalizations).…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, it offers a complexity-accuracy trade-off. Moreover, the C-SECSI framework is capable of jointly decomposing tensors with different SNRs (Signal to Noise Rations), i.e., a normalization with respect to the noise variance is not required [2].…”

Section: Introductionmentioning

confidence: 99%

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Analysis of the photic driving effect via joint EEG and MEG data processing based on the coupled CP decomposition

Naskovska

Korobkov

Haardt

et al. 2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-There are many combined signal processing applications such as the joint processing of EEG (Electroencephalogram) and MEG (Magnetoencephalogram) data that can benefit from coupled CP (Canonical Polyadic) tensor decompositions. The coupled CP decomposition jointly decomposes tensors that have at least one factor matrix in common. The C-SECSI (Coupled -Semi-Algebraic framework for approximate CP decomposition via SImultaneaous matrix diagonalization) framework provides a semi-algebraic solution for the coupled CP decomposition of noise corrupted low-rank tensors. The C-SECSI framework efficiently computes the factor matrices even in ill-posed scenarios with an adjustable complexity-accuracy trade-off. In this paper, we present a reliability test for the C-SECSI framework that can improve the model order estimation. Moreover, we analyse the photic driving effect from simultaneously recorded EEG and MEG data using the C-SECSI framework. The EEG and MEG data used in the analysis are obtained by stimulating volunteers with flickering light at different frequencies that are multiples of the individual alpha frequency of each volunteer.

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Section: Tensor Algebra and Coupled Cp Decompositionmentioning

confidence: 99%

Section: Tensor Algebra and Coupled Cp Decompositionmentioning

confidence: 99%

Section: Tensor Algebra and Coupled Cp Decompositionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Analysis of the photic driving effect via joint EEG and MEG data processing based on the coupled CP decomposition

Naskovska

Korobkov

Haardt

et al. 2017

2017 25th European Signal Processing Conference (EUSIPCO)

Self Cite

View full text Add to dashboard Cite

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Robust coupled tensor decomposition and feature extraction for multimodal medical data

Zhao

Gahrooei

Gaw

2022

IISE Transactions on Healthcare Systems Engineering

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A Survey on Tensor Techniques and Applications in Machine Learning

Wang

et al. 2019

IEEE Access

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This survey gives a comprehensive overview of tensor techniques and applications in machine learning. Tensor represents higher order statistics. Nowadays, many applications based on machine learning algorithms require a large amount of structured high-dimensional input data. As the set of data increases, the complexity of these algorithms increases exponentially with the increase of vector size. Some scientists found that using tensors instead of the original input vectors can effectively solve these high-dimensional problems. This survey introduces the basic knowledge of tensor, including tensor operations, tensor decomposition, some tensor-based algorithms, and some applications of tensor in machine learning and deep learning for those who are interested in learning tensors. The tensor decomposition is highlighted because it can effectively extract structural features of data and many algorithms and applications are based on tensor decomposition. The organizational framework of this paper is as follows. In part one, we introduce some tensor basic operations, including tensor decomposition. In part two, applications of tensor in machine learning and deep learning, including regression, supervised classification, data preprocessing, and unsupervised classification based on low rank tensor approximation algorithms are introduced detailly. Finally, we briefly discuss urgent challenges, opportunities and prospects for tensor.

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Extension of the semi-algebraic framework for approximate CP decompositions via simultaneous matrix diagonalization to the efficient calculation of coupled CP decompositions

Cited by 11 publications

References 11 publications

Analysis of the photic driving effect via joint EEG and MEG data processing based on the coupled CP decomposition

Analysis of the photic driving effect via joint EEG and MEG data processing based on the coupled CP decomposition

Robust coupled tensor decomposition and feature extraction for multimodal medical data

A Survey on Tensor Techniques and Applications in Machine Learning

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