Tensors for Data Processing

Tensors for Data Processing

Theory, Methods, and Applications

1st Edition - October 21, 2021

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  • Editor: Yipeng Liu
  • Paperback ISBN: 9780128244470
  • eBook ISBN: 9780323859653

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Description

Tensors for Data Processing: Theory, Methods and Applications presents both classical and state-of-the-art methods on tensor computation for data processing, covering computation theories, processing methods, computing and engineering applications, with an emphasis on techniques for data processing. This reference is ideal for students, researchers and industry developers who want to understand and use tensor-based data processing theories and methods. As a higher-order generalization of a matrix, tensor-based processing can avoid multi-linear data structure loss that occurs in classical matrix-based data processing methods. This move from matrix to tensors is beneficial for many diverse application areas, including signal processing, computer science, acoustics, neuroscience, communication, medical engineering, seismology, psychometric, chemometrics, biometric, quantum physics and quantum chemistry.

Key Features

  • Provides a complete reference on classical and state-of-the-art tensor-based methods for data processing
  • Includes a wide range of applications from different disciplines
  • Gives guidance for their application

Readership

Graduate students and researchers in computer science and engineering

Table of Contents

  • Cover image
  • Title page
  • Table of Contents
  • Copyright
  • List of contributors
  • Preface
  • Chapter 1: Tensor decompositions: computations, applications, and challenges
  • Abstract
  • 1.1. Introduction
  • 1.2. Tensor operations
  • 1.3. Tensor decompositions
  • 1.4. Tensor processing techniques
  • 1.5. Challenges
  • References
  • Chapter 2: Transform-based tensor singular value decomposition in multidimensional image recovery
  • Abstract
  • 2.1. Introduction
  • 2.2. Recent advances of the tensor singular value decomposition
  • 2.3. Transform-based t-SVD
  • 2.4. Numerical experiments
  • 2.5. Conclusions and new guidelines
  • References
  • Chapter 3: Partensor
  • Abstract
  • Acknowledgement
  • 3.1. Introduction
  • 3.2. Tensor decomposition
  • 3.3. Tensor decomposition with missing elements
  • 3.4. Distributed memory implementations
  • 3.5. Numerical experiments
  • 3.6. Conclusion
  • References
  • Chapter 4: A Riemannian approach to low-rank tensor learning
  • Abstract
  • 4.1. Introduction
  • 4.2. A brief introduction to Riemannian optimization
  • 4.3. Riemannian Tucker manifold geometry
  • 4.4. Algorithms for tensor learning problems
  • 4.5. Experiments
  • 4.6. Conclusion
  • References
  • Chapter 5: Generalized thresholding for low-rank tensor recovery: approaches based on model and learning
  • Abstract
  • 5.1. Introduction
  • 5.2. Tensor singular value thresholding
  • 5.3. Thresholding based low-rank tensor recovery
  • 5.4. Generalized thresholding algorithms with learning
  • 5.5. Numerical examples
  • 5.6. Conclusion
  • References
  • Chapter 6: Tensor principal component analysis
  • Abstract
  • 6.1. Introduction
  • 6.2. Notations and preliminaries
  • 6.3. Tensor PCA for Gaussian-noisy data
  • 6.4. Tensor PCA for sparsely corrupted data
  • 6.5. Tensor PCA for outlier-corrupted data
  • 6.6. Other tensor PCA methods
  • 6.7. Future work
  • 6.8. Summary
  • References
  • Chapter 7: Tensors for deep learning theory
  • Abstract
  • 7.1. Introduction
  • 7.2. Bounding a function's expressivity via tensorization
  • 7.3. A case study: self-attention networks
  • 7.4. Convolutional and recurrent networks
  • 7.5. Conclusion
  • References
  • Chapter 8: Tensor network algorithms for image classification
  • Abstract
  • 8.1. Introduction
  • 8.2. Background
  • 8.3. Tensorial extensions of support vector machine
  • 8.4. Tensorial extension of logistic regression
  • 8.5. Conclusion
  • References
  • Chapter 9: High-performance tensor decompositions for compressing and accelerating deep neural networks
  • Abstract
  • 9.1. Introduction and motivation
  • 9.2. Deep neural networks
  • 9.3. Tensor networks and their decompositions
  • 9.4. Compressing deep neural networks
  • 9.5. Experiments and future directions
  • References
  • Chapter 10: Coupled tensor decompositions for data fusion
  • Abstract
  • Acknowledgements
  • 10.1. Introduction
  • 10.2. What is data fusion?
  • 10.3. Decompositions in data fusion
  • 10.4. Applications of tensor-based data fusion
  • 10.5. Fusion of EEG and fMRI: a case study
  • 10.6. Data fusion demos
  • 10.7. Conclusion and prospects
  • References
  • Chapter 11: Tensor methods for low-level vision
  • Abstract
  • Acknowledgements
  • 11.1. Low-level vision and signal reconstruction
  • 11.2. Methods using raw tensor structure
  • 11.3. Methods using tensorization
  • 11.4. Examples of low-level vision applications
  • 11.5. Remarks
  • References
  • Chapter 12: Tensors for neuroimaging
  • Abstract
  • 12.1. Introduction
  • 12.2. Neuroimaging modalities
  • 12.3. Multidimensionality of the brain
  • 12.4. Tensor decomposition structures
  • 12.5. Applications of tensors in neuroimaging
  • 12.6. Future challenges
  • 12.7. Conclusion
  • References
  • Chapter 13: Tensor representation for remote sensing images
  • Abstract
  • 13.1. Introduction
  • 13.2. Optical remote sensing: HSI and MSI fusion
  • 13.3. Polarimetric synthetic aperture radar: feature extraction
  • References
  • Chapter 14: Structured tensor train decomposition for speeding up kernel-based learning
  • Abstract
  • 14.1. Introduction
  • 14.2. Notations and algebraic background
  • 14.3. Standard tensor decompositions
  • 14.4. Dimensionality reduction based on a train of low-order tensors
  • 14.5. Tensor train algorithm
  • 14.6. Kernel-based classification of high-order tensors
  • 14.7. Experiments
  • 14.8. Conclusion
  • References
  • Index

Product details

  • No. of pages: 596
  • Language: English
  • Copyright: © Academic Press 2021
  • Published: October 21, 2021
  • Imprint: Academic Press
  • Paperback ISBN: 9780128244470
  • eBook ISBN: 9780323859653

About the Editor

Yipeng Liu

Yipeng Liu received the BSc degree in biomedical engineering and the PhD degree in information and communication engineering from University of Electronic Science and Technology of China (UESTC), Chengdu, in 2006 and 2011, respectively. From 2011 to 2014, he was a postdoctoral research fellow at University of Leuven, Leuven, Belgium. Since 2014, he has been an associate professor with UESTC, Chengdu, China. His research interest is tensor signal processing. He has authored or co-authored over 70 publication, inculding a series of papers on sparse tensor, tensor completion, tensor PCA, tensor regression, and so on. He has served as an associate editor for IEEE Signal Processing Letters (2019 - now), an editorial board member for Heliyon (2018 - 2019), and the managing guest editor for the special issue “tensor image processing” in Signal Processing: Image Communication. He has served on technical or program committees for 5 international conferences. He is an IEEE senior member, a member of the Multimedia Technology Technical Committee of Chinese Computer Federation, and a member of China Society of Image and Graphics on Youth Working Committee. He has given give tutorials for a few international conferences, including 2019 IEEE International Symposium on Circuits and Systems (ISCAS), 2019 IEEE International Workshop on Signal Processing Systems (SiPS), and 11th Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA ASC), and is going to give tutorials on the 27th IEEE International Conference on Image Processing (ICIP 2020) and The 2020 IEEE Symposium Series on Computational Intelligence (IEEE SSCI 2020). He has been teaching optimization theory and applications for graduates since 2015, and received the 8th University Teaching Achievement Award in 2016.

Affiliations and Expertise

Associate Professor, UESTC, Chengdu, China

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