Tensors for Data Processing: Theory, Methods, and Applications
- Length: 596 pages
- Edition: 1
- Language: English
- Publisher: Academic Press
- Publication Date: 2021-11-15
- ISBN-10: 012824447X
- ISBN-13: 9780128244470
- Sales Rank: #0 (See Top 100 Books)
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.
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
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