Aimed at students in mathematics, computer science, statistics, engineering, and physical and life sciences, this book introduces the foundations of tensor decompositions, a data analysis methodology ubiquitous in machine learning, signal processing, neuroscience, quantum computing, financial analysis, market analysis, and image processing.
Aimed at students in mathematics, computer science, statistics, engineering, and physical and life sciences, this book introduces the foundations of tensor decompositions, a data analysis methodology ubiquitous in machine learning, signal processing, neuroscience, quantum computing, financial analysis, market analysis, and image processing.
Grey Ballard is Associate Professor of Computer Science at Wake Forest University. He specializes in numerical linear algebra, high performance computing, and computational science, with much of his work focusing on numerical methods and software for tensor decompositions. His work has been recognized with a National Science Foundation (NSF) Faculty Early Career Development (CAREER) award, a SIAM Linear Algebra Best Paper Prize, and conference best paper awards at the ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), IEEE International Parallel & Distributed Processing Symposium (IPDPS), and IEEE International Conference on Data Mining (ICDM).
Inhaltsangabe
Preface I. Tensor Basics: 1. Tensors and their subparts 2. Indexing and reshaping tensors 3. Tensor operations II. Tucker Decomposition: 4. Tucker decomposition 5. Tucker tensor structure 6. Tucker algorithms 7. Tucker approximation error 8. Tensor train decomposition III. CP Decomposition: 9. Canonical polyacidic (CP) decomposition 10. Kruskal tensor structure 11. CP alternating least squares (CP-ALS) optimization 12. CP gradient-based optimization (CP-OPT) 13. CP nonlinear least squares (CP-NLS) optimization 14. CP algorithms for incomplete or scarce data 15. Generalized CP (GCP) decomposition 16. CP tensor rank and special topics IV. Closing Observations: 17. Closing observations V. Review Materials: A. Numerical linear algebra B. Optimization principles and methods C. Some statistics and probability Bibliography Index.
Preface I. Tensor Basics: 1. Tensors and their subparts 2. Indexing and reshaping tensors 3. Tensor operations II. Tucker Decomposition: 4. Tucker decomposition 5. Tucker tensor structure 6. Tucker algorithms 7. Tucker approximation error 8. Tensor train decomposition III. CP Decomposition: 9. Canonical polyacidic (CP) decomposition 10. Kruskal tensor structure 11. CP alternating least squares (CP-ALS) optimization 12. CP gradient-based optimization (CP-OPT) 13. CP nonlinear least squares (CP-NLS) optimization 14. CP algorithms for incomplete or scarce data 15. Generalized CP (GCP) decomposition 16. CP tensor rank and special topics IV. Closing Observations: 17. Closing observations V. Review Materials: A. Numerical linear algebra B. Optimization principles and methods C. Some statistics and probability Bibliography Index.
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