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Fast Hankel tensor-vector product and its application to exponential data fitting

Weiyang Ding, Liqun Qi, Yimin Wei
2015 Numerical Linear Algebra with Applications  
We propose an analogous fast algorithm for Hankel tensor-vector products, which has its application to exponential data fitting. We first introduce Papy et al.'  ...  EXPONENTIAL DATA FITTING We begin with one of the sources of Hankel tensors and see where we need fast Hankel tensor-vector products.  ...  The Hankel tensor for 1D exponential data fitting is of size 15 15 15 , and the BHHB tensor for 2D exponential data fitting is of level-1 size 5 5 5 and level-2 size 6 6 6.  ... 
doi:10.1002/nla.1970 fatcat:dquhk2kvjjc4hlv5mk7xmz253m

Fast Hankel Tensor-Vector Products and Application to Exponential Data Fitting [article]

Weiyang Ding, Liqun Qi, Yimin Wei
2014 arXiv   pre-print
Finally, we apply the fast algorithm to exponential data fitting and the block version to 2D exponential data fitting for higher performance.  ...  This paper is contributed to a fast algorithm for Hankel tensor-vector products.  ...  Acknowledgements Weiyang Ding would like to thank Prof. Sanzheng Qiao for the useful discussions on fast algorithms for Hankel matrices. We also thank Professors Lars Eldén and Michael K.  ... 
arXiv:1401.6238v1 fatcat:2i2msuh6y5c33iavahbafyes3e

Computing Extreme Eigenvalues of Large Scale Hankel Tensors

Yannan Chen, Liqun Qi, Qun Wang
2016 Journal of Scientific Computing  
We introduce a fast computational framework for products of a well-structured Hankel tensor and vectors in Sect. 2. The computational cost is cheap.  ...  Large scale tensors, including large scale Hankel tensors, have many applications in science and engineering.  ...  Weiyang Ding and Dr. Ziyan Luo for the discussion on numerical experiments, and two referees for their valuable comments.  ... 
doi:10.1007/s10915-015-0155-8 fatcat:dpndi2m7qbh7bonaiyt6pyaiv4

Hankel Matrix Nuclear Norm Regularized Tensor Completion for $N$-dimensional Exponential Signals

Jiaxi Ying, Hengfa Lu, Qingtao Wei, Jian-Feng Cai, Di Guo, Jihui Wu, Zhong Chen, Xiaobo Qu
2017 IEEE Transactions on Signal Processing  
For fast data acquisition or other inevitable reasons, however, only a small amount of samples may be acquired and thus how to recover the full signal becomes an active research topic.  ...  exponential factor vectors.  ...  Altogether, our proposed approach minimizes an objective function consisting of a least square fitting to the sampled data, where the signal tensor is written in a CP decompostion form, and Hankel matrix  ... 
doi:10.1109/tsp.2017.2695566 fatcat:i3inmyauofafbckermbdzv4pju

Higher Order Tensor-Based Method for Delayed Exponential Fitting

Rmy Boyer, Lieven De Lathauwer, Karim Abed-Meraim
2007 IEEE Transactions on Signal Processing  
Higher-order tensor-based method for delayed exponential fitting.  ...  In this contribution, we propose solutions based on the approximation of a partially structured Hankel-type tensor on which the data are mapped.  ...  Our approach is, thus, fundamentally different from fitting to the data tensor a minimal sum of rank-1 tensors (the latter approach is known as "fitting a canonical decomposition" or "parallel factor analysis  ... 
doi:10.1109/tsp.2007.893981 fatcat:5kuhqvxu3vcphkogjh7632t42a

Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 2 Applications and Future Perspectives

Andrzej Cichocki, Namgil Lee, Ivan Oseledets, Anh-Huy Phan, Qibin Zhao, Masashi Sugiyama, Danilo P. Mandic
2017 Foundations and Trends® in Machine Learning  
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  ...  and data analytics.  ...  For example, the Hankel and Toeplitz matrices/tensors of an exponential function, v k az k¡1 , are rank-1 matrices/tensors, and consequently Hankel matrices/tensors of sums and/or products of exponentials  ... 
doi:10.1561/2200000067 fatcat:3dcqhbz3fbho3etflurfosvunq

Tensor Based Method for Residual Water Suppression in $^{1}$ H Magnetic Resonance Spectroscopic Imaging

Bharath Halandur Nagaraja, Otto Debals, Diana M. Sima, Uwe Himmelreich, Lieven De Lathauwer, Sabine Van Huffel
2018 IEEE Transactions on Biomedical Engineering  
A canonical polyadic decomposition is applied on the tensor to extract the water component and to, subsequently, remove it from the original MRSI signals.  ...  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.  ...  ACKNOWLEDGMENT The authors would like to thank the University Hospitals of Leuven for data acquisition.  ... 
doi:10.1109/tbme.2018.2850911 pmid:29993479 fatcat:ybwvlhuanjggxjvkv7yyg3qvji

Block term decomposition for modelling epileptic seizures

Borbála Hunyadi, Daan Camps, Laurent Sorber, Wim Van Paesschen, Maarten De Vos, Sabine Van Huffel, Lieven De Lathauwer
2014 EURASIP Journal on Advances in Signal Processing  
Here, we present the application of a recently introduced technique, called block term decomposition (BTD) to separate EEG tensors into rank-(L r , L r , 1) terms, allowing to model more variability in  ...  the data than what would be possible with CPD.  ...  Acknowledgements We express our thanks to the following:  ... 
doi:10.1186/1687-6180-2014-139 fatcat:6s6ft3zd7va47ipekvaje5u74u

An efficient quantum algorithm for spectral estimation

Adrian Steffens, Patrick Rebentrost, Iman Marvian, Jens Eisert, Seth Lloyd
2017 New Journal of Physics  
accessible and an alternative method to efficiently exponentiate non-Hermitian matrices.  ...  Along the way, we develop techniques that are expected to be useful for other quantum algorithms as well - consecutive phase estimations to efficiently make products of asymmetric low rank matrices classically  ...  SL and PR were supported by ARO and AFOSR. JE thanks  ... 
doi:10.1088/1367-2630/aa5e48 fatcat:hecvuiv4ujgwzmp7lf4jz5nevq

A Tensor-Based Method for Large-Scale Blind Source Separation Using Segmentation

Martijn Bousse, Otto Debals, Lieven De Lathauwer
2017 IEEE Transactions on Signal Processing  
This deterministic tensorization technique is called segmentation and is closely related to Hankel-based tensorization.  ...  We propose a new deterministic method for blind source separation that exploits the low-rank structure, enabling a unique separation of the source signals and providing a way to cope with large-scale data  ...  Tensor decompositions An N th-order tensor has rank one if it can be written as the outer product of N nonzero vectors.  ... 
doi:10.1109/tsp.2016.2617858 fatcat:fhfuuswuojhtlgjx7c4s4uj64a

Inheritance Properties and Sum-of-Squares Decomposition of Hankel Tensors: Theory and Algorithms [article]

Weiyang Ding, Liqun Qi, Yimin Wei
2015 arXiv   pre-print
In this paper, we show that if a lower-order Hankel tensor is positive semi-definite (or positive definite, or negative semi-definite, or negative definite, or SOS), then its associated higher-order Hankel  ...  tensor with the same generating vector, where the higher order is a multiple of the lower order, is also positive semi-definite (or positive definite, or negative semi-definite, or negative definite,  ...  Acknowledgements We would like to thank Prof. Man-Duen Choi and Dr. Ziyan Luo for their helpful discussions. We would also like to thank the editor, Prof.  ... 
arXiv:1505.02528v4 fatcat:h75oktanszhvbldzm6ps5v3dpi

Blind Source Separation in Persistent Atrial Fibrillation Electrocardiograms Using Block-Term Tensor Decomposition with Lwner Constraints

Pedro Marinho Ramos Deoliveira, Jose Henrique De Morais Goulart, Carlos Alexandre Rolim Fernandes, Vicente Zarzoso
2021 IEEE journal of biomedical and health informatics  
However, persistent forms of AF are characterized by short R-R intervals and very disorganized (or weak) AA, making it difficult to model AA directly and perform its successful extraction through Hankel-BTD  ...  suited to the estimation of exponential models like AA during AF.  ...  Such issues make it difficult to fit the AA signals to this exponential model, compromising the AA extraction via Hankel-BTD. C.  ... 
doi:10.1109/jbhi.2021.3108699 pmid:34460408 fatcat:xqip23wg5japtbqezhyuqe5stu

Tensor Decompositions for Signal Processing Applications: From two-way to multiway component analysis

Andrzej Cichocki, Danilo Mandic, Lieven De Lathauwer, Guoxu Zhou, Qibin Zhao, Cesar Caiafa, HUY ANH PHAN
2015 IEEE Signal Processing Magazine  
learning applications; these benefits also extend to vector/matrix data through tensorization.  ...  to advanced cause-effect and multi-view data analysis schemes.  ...  He worked as a deputy head of the Research and Development Department, Broadcast Research and Application Center, Vietnam Television, and is currently a research scientist at the Laboratory for Advanced  ... 
doi:10.1109/msp.2013.2297439 fatcat:gcyacttbvbhtjcjfr4hdfzdciy

Derivation and Analysis of Fast Bilinear Algorithms for Convolution [article]

Caleb Ju, Edgar Solomonik
2020 arXiv   pre-print
The prevalence of convolution in applications within signal processing, deep neural networks, and numerical solvers has motivated the development of numerous fast convolution algorithms.  ...  We provide new derivations, which predominantly leverage matrix and tensor algebra, to describe the Winograd family of convolution algorithms as well as reductions between 1D and multidimensional convolution  ...  We would like to thank Hung Woei Neoh for helpful discussions and the anonymous referees for providing valuable feedback that helped improve this manuscript.  ... 
arXiv:1910.13367v2 fatcat:s7n76pak3fejdpo4ey46klrsvu

Gaussians on Riemannian Manifolds: Applications for Robot Learning and Adaptive Control [article]

Sylvain Calinon
2020 arXiv   pre-print
Two examples of applications are presented, involving the control of a prosthetic hand from surface electromyography (sEMG) data, and the teleoperation of a bimanual underwater robot.  ...  This article presents an overview of robot learning and adaptive control applications that can benefit from a joint use of Riemannian geometry and probabilistic representations.  ...  On a Riemannian manifold, the metric tensor induces a positive definite inner product on Fig. 2 .  ... 
arXiv:1909.05946v4 fatcat:ojaty7ptljdblbrt7p6jwiom3a
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