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Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 2 Applications and Future Perspectives
2017
Foundations and Trends® in Machine Learning
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It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning ...
partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. ...
Summary This chapter has introduced several common tensorization methods, together with their properties and illustrative applications in blind source separation, blind identification, denoising, and harmonic ...
doi:10.1561/2200000067
fatcat:3dcqhbz3fbho3etflurfosvunq
Löwner-Based Blind Signal Separation of Rational Functions With Applications
2016
IEEE Transactions on Signal Processing
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Finally, the technique is illustrated for fetal electrocardiogram extraction and with an application in the domain of fluorescence spectroscopy, enabling the identification of chemical analytes using only ...
The technique uses a low-rank decomposition on the tensorized version of the observed data matrix. The deterministic tensorization with Löwner matrices is comprehensively analyzed in this paper. ...
His research concerns the tensorization of matrix data, with further interests sin tensor decompositions, optimization, blind signal separation and blind system identification. ...
doi:10.1109/tsp.2015.2500179
fatcat:dxqsin3bbzfs7bnt5k3li2i2qu
Performance estimation for tensor CP decomposition with structured factors
2015
2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
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Structured CPDs, i.e. with Toeplitz, circulant, or Hankel factor matrices, are often encountered in signal processing applications. ...
on one hand, and an Hankel factor on the other hand. ...
In this paper, we derive the CRB for tensor CP decomposition with both structured (Hankel, Toeplitz and Toeplitz circulant) and unstructured factors. ...
doi:10.1109/icassp.2015.7178618
dblp:conf/icassp/BoizardBFCC15
fatcat:nfndcqmosrgsllekbw35rpyqvi
Decomposing tensors with structured matrix factors reduces to rank-1 approximations
2010
2010 IEEE International Conference on Acoustics, Speech and Signal Processing
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some structure, such as block-Hankel, triangular, band, etc. ...
Tensor decompositions are very attractive in the fields of antenna array processing [6] and digital communications [7], ...
Factor matrices appearing in the tensor decomposition can be structured [4] [9] , and can have the very particular structure of banded triangular Toeplitz if Blind Identification of a SISO FIR channel ...
doi:10.1109/icassp.2010.5495816
dblp:conf/icassp/ComonST10
fatcat:ypciymdicrcefechikbq2o56uq
Tensor Based Method for Residual Water Suppression in $^{1}$ H Magnetic Resonance Spectroscopic Imaging
2018
IEEE Transactions on Biomedical Engineering
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Index Terms-Canonical polyadic decomposition, magnetic resonance spectroscopic imaging, Löwner matrix, Hankel matrix, blind source separation. Manuscript ...
Conclusion: The tensor-based Löwner method has better performance in suppressing residual water in MRSI signals as compared to the widely used subspace-based Hankel singular value decomposition method. ...
Hankel matrices are used in many applications such as system identification, coding theory. ...
doi:10.1109/tbme.2018.2850911
pmid:29993479
fatcat:ybwvlhuanjggxjvkv7yyg3qvji
Tensor decompositions and data fusion in epileptic electroencephalography and functional magnetic resonance imaging data
2016
Wiley Interdisciplinary Reviews Data Mining and Knowledge Discovery
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Finding an appropriate tensor representation, suitable tensor model, and interpretation are application dependent choices, which require expertise both in neuroscience and in multilinear algebra. ...
The aim of this paper is to provide a general guideline for these choices and illustrate them through successful applications in epilepsy. ...
This paper reflects only the authors' views and the Union is not liable for any use that may be made of the contained information. ...
doi:10.1002/widm.1197
fatcat:fr4mjfg5gffpvasjbc6hozyxse
Non-Iterative Solution For Parafac With Toeplitz Matrix Factors
2009
Zenodo
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Publication in the conference proceedings of EUSIPCO, Glasgow, Scotland, 2009 ...
In a future work, robustness to noise, extension to higher-order tensors, and application to block-structured nonlinear system identification will be considered. ...
It can also be applied to PARAFAC decompositions with Hankel factors. ...
doi:10.5281/zenodo.41515
fatcat:7suqgycm55ccjfcvpbyz7rxqk4
A Tensor-Based Method for Large-Scale Blind Source Separation Using Segmentation
2017
IEEE Transactions on Signal Processing
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This deterministic tensorization technique is called segmentation and is closely related to Hankel-based tensorization. ...
We explain that our method reformulates the blind source separation problem as the computation of a tensor decomposition, after reshaping the observed data matrix into a tensor. ...
Several ICA methods use higher-order statistics (HOS) in order to tensorize the BSS problem and then apply a tensor decomposition to uniquely identify the sources. ...
doi:10.1109/tsp.2016.2617858
fatcat:fhfuuswuojhtlgjx7c4s4uj64a
Blind Channel Identification Of Miso Systems Based On The Cp Decomposition Of Cumulant Tensors
2011
Zenodo
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Publication in the conference proceedings of EUSIPCO, Barcelona, Spain, 2011 ...
It was shown in [7] that the problem of blind SISO identification can be reformulated as a problem of computing the Parallel Factor (Parafac known also as CP) decomposition of a third-order (2L + 1) ...
Moreover, factors in the Parafac decomposition have a Hankel structure. This paper is possibly a first attempt to find non-linear optimization solutions for MISO case. ...
doi:10.5281/zenodo.42520
fatcat:h7f4fm2ehbh2zjuiadv33ekvfe
Tensor Based Singular Spectrum Analysis for Automatic Scoring of Sleep EEG
2015
IEEE transactions on neural systems and rehabilitation engineering
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As an important application, sleep EEG has been analysed and the stages of sleep for the subjects in normal condition, with sleep restriction, and with sleep extension have been accurately estimated and ...
A new supervised approach for decomposition of single channel signal mixtures is introduced in this paper. ...
TENSOR-BASED SSA Application of SSA to real data does not exploit the inherent nonstationarity and therefore may fail in actual data decomposition. ...
doi:10.1109/tnsre.2014.2329557
pmid:24951703
fatcat:oylgevbu45ctxp7tzcvqcrwvhi
Tensor decompositions with banded matrix factors
2013
Linear Algebra and its Applications
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First, we develop methods for the computation of CPDs with one banded matrix factor. It results in best rank-1 tensor approximation problems. ...
In many practical problems involving tensor decompositions such as signal processing, some of the matrix factors are banded. ...
Acknowledgments The authors thank the reviewers for their careful reading and relevant and helpful comments. ...
doi:10.1016/j.laa.2011.10.044
fatcat:m7xqicsn65cghkgwp2fugoffkq
Overview of constrained PARAFAC models
2014
EURASIP Journal on Advances in Signal Processing
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In this paper, we present an overview of constrained PARAFAC models where the constraints model linear dependencies among columns of the factor matrices of the tensor decomposition, or alternatively, the ...
New tensor models, called nested Tucker models and block PARALIND/CONFAC models, are also introduced. A link between PARATUCK models and constrained PARAFAC models is then established. ...
Cichocki for his useful comments and suggestions.
Author details ...
doi:10.1186/1687-6180-2014-142
fatcat:fogozht5uvffxmirsetu4hg62q
Constrained Subspace Method for the Identification of Structured State-Space Models
2019
IEEE Transactions on Automatic Control
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To alleviate this problem, the linear regression formulation is imposed by structured and low-rank constraints in terms of a finite set of system Markov parameters and the user specified model parameters ...
The new identification framework relies on a subspace inspired linear regression problem which may not yield a consistent estimate in the presence of process noise. ...
Hankel matrix factorization with structural constraints The block Hankel matrix H u in the optimization problem (22) possesses a structured and low-rank factorization. ...
doi:10.1109/tac.2019.2957703
fatcat:tmvbzega6jez7bxpijwhvimna4
Hankel low-rank approximation and completion in time series analysis and forecasting: a brief review
[article]
2022
arXiv
pre-print
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In this paper we offer a review and bibliography of work on Hankel low-rank approximation and completion, with particular emphasis on how this methodology can be used for time series analysis and forecasting ...
Key theorems are provided, and the paper closes with some expository examples. ...
More generally nuclear norm relaxation has proved a useful tool in: spectral estimation [3] , recommender systems [65] , system identification [79] and several other application areas. ...
arXiv:2206.05103v1
fatcat:2ohsrphxjfc4pf2v6kv4am7hnq
An Algebraic Solution for the Candecomp/PARAFAC Decomposition with Circulant Factors
2014
SIAM Journal on Matrix Analysis and Applications
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The Candecomp/PARAFAC decomposition (CPD) is an important mathematical tool used in several fields of application. ...
In some practical contexts, the data tensors of interest admit decompositions constituted by matrix factors with particular structure. ...
For instance, in [14] the third-order core tensors of block Tucker models are characterized by matrix slices having Hankel and Vandermonde forms, which is taken into account for deriving a specialized ...
doi:10.1137/140955963
fatcat:3rvzdfq655eg5ikydzyiswce2q
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