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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.
List of contents
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.
About the author
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).Tamara G. Kolda is an independent consultant under the auspices of her company, MathSci.ai. Her research background is in numerical linear algebra, optimization, data science, and scientific software, and she is well known for her pioneering algorithmic and software work in tensor decompositions. She has been honoured with various recognitions, notably her appointments as member of the US National Academy of Engineering (NAE), Fellow of the Society for Industrial and Applied Mathematics (SIAM), and Fellow of the Association for Computing Machinery (ACM). She helped to create and served as founding editor-in-chief of the SIAM Journal on Mathematics of Data Science.
