Matrix and tensor decompositions in signal processing . Volume 2 / / Gerard Favier

• Autore: Favier Gérard
• Pubblicazione: London, England : , : ISTE Ltd, , [2021]; ℗♭2021
• Descrizione fisica: 1 online resource (386 pages)
• Disciplina: 005.1
• Soggetto topico: Computer algorithms
• Soggetto genere / forma: Electronic books.
• Nota di contenuto: 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.
• Titolo autorizzato: Matrix and Tensor Decompositions in Signal Processing
• ISBN: 1-119-70098-1; 1-119-70099-X; 1-119-70096-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910555065903321
• Lo trovi qui: Univ. Federico II