Tensors for Data Processing: Theory, Methods, and Applications 1st Edition by Yipeng 9780323859653 0323859658

Tensors for Data Processing: Theory, Methods, and Applications 1st Edition Yipeng Liu (Ed.) – Ebook Instant Download/Delivery ISBN(s): 9780323859653, 0323859658

Product details:

• ISBN 10: 0323859658
• ISBN 13: 9780323859653
• Author: Yipeng 

Tensors for Data Processing
Theory, Methods, and Applications

Table contents:

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

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