Matrix and tensor decompositions in signal processing. Volume 2

Matrix and tensor decompositions in signal processing Volume 2 Volume 2 /

The second volume will deal with a presentation of the main matrix and tensor decompositions and their properties of uniqueness, as well as very useful tensor networks for the analysis of massive data. Parametric estimation algorithms will be presented for the identification of the main tensor decom...

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Detalles Bibliográficos
Otros Autores: Favier, Gérard, author (author)
Formato: Libro electrónico
Idioma:Inglés
Publicado: London, England : ISTE Ltd [2021]
Colección:Digital signal and image processing series. Matrices and tensors in signal processing set.
Materias:
Signal processing > Digital techniques > Mathematics.
Computer algorithms.
Calculus of tensors.
Matrices.
Algorithms.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009724214906719
Tabla de Contenidos:
  • Intro
  • Table of Contents
  • Title Page
  • Copyright
  • Introduction
  • I.1. What are the advantages of tensor approaches?
  • I.2. For what uses?
  • I.3. In what fields of application?
  • I.4. With what tensor decompositions?
  • I.5. With what cost functions and optimization algorithms?
  • I.6. Brief description of content
  • 1 Matrix Decompositions
  • 1.1. Introduction
  • 1.2. Overview of the most common matrix decompositions
  • 1.3. Eigenvalue decomposition
  • 1.4. URVH decomposition
  • 1.5. Singular value decomposition
  • 1.6. CUR decomposition
  • 2 Hadamard, Kronecker and Khatri-Rao Products
  • 2.1. Introduction
  • 2.2. Notation
  • 2.3. Hadamard product
  • 2.4. Kronecker product
  • 2.5. Kronecker sum
  • 2.6. Index convention
  • 2.7. Commutation matrices
  • 2.8. Relations between the diag operator and the Kronecker product
  • 2.9. Khatri-Rao product
  • 2.10. Relations between vectorization and Kronecker and Khatri-Rao products
  • 2.11. Relations between the Kronecker, Khatri-Rao and Hadamard products
  • 2.12. Applications
  • 3 Tensor Operations
  • 3.1. Introduction
  • 3.2. Notation and particular sets of tensors
  • 3.3. Notion of slice
  • 3.4. Mode combination
  • 3.5. Partitioned tensors or block tensors
  • 3.6. Diagonal tensors
  • 3.7. Matricization
  • 3.8. Subspaces associated with a tensor and multilinear rank
  • 3.9. Vectorization
  • 3.10. Transposition
  • 3.11. Symmetric/partially symmetric tensors
  • 3.12. Triangular tensors
  • 3.13. Multiplication operations
  • 3.14. Inverse and pseudo-inverse tensors
  • 3.15. Tensor decompositions in the form of factorizations
  • 3.16. Inner product, Frobenius norm and trace of a tensor
  • 3.17. Tensor systems and homogeneous polynomials
  • 3.18. Hadamard and Kronecker products of tensors
  • 3.19. Tensor extension
  • 3.20. Tensorization
  • 3.21. Hankelization.
  • 4 Eigenvalues and Singular Values of a Tensor
  • 4.1. Introduction
  • 4.2. Eigenvalues of a tensor of order greater than two
  • 4.3. Best rank-one approximation
  • 4.4. Orthogonal decompositions
  • 4.5. Singular values of a tensor
  • 5 Tensor Decompositions
  • 5.1. Introduction
  • 5.2. Tensor models
  • 5.3. Examples of tensor models
  • Appendix Random Variables and Stochastic Processes
  • A1.1. Introduction
  • A1.2. Random variables
  • A1.3. Discrete-time random signals
  • A1.4. Application to system identification
  • References
  • Index
  • End User License Agreement.

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