High-Dimensional Data Analysis with Low-Dimensional Models
Principles, Computation, and Applications

Connects fundamental mathematical theory with real-world problems, through efficient and scalable optimization algorithms.

John Wright (Author), Yi Ma (Author)

9781108489737, Cambridge University Press

Hardback, published 13 January 2022

650 pages
25.1 x 17.5 x 3.6 cm, 1.43 kg

'At the very core of our ability to process data stands the fact that sources of information are structured. Modeling data, explicitly or implicitly, is our way of exposing this structure and exploiting it, being the essence of the fields of signal and image processing and machine learning. The past two decades have brought a revolution to our understanding of these facts, and this 'must-read' book provides the foundations of these recent developments, covering theoretical, numerical, and applicative aspects of this field in a thorough and clear manner.' Michael Elad, Technion – Israel Institute of Technology

Connecting theory with practice, this systematic and rigorous introduction covers the fundamental principles, algorithms and applications of key mathematical models for high-dimensional data analysis. Comprehensive in its approach, it provides unified coverage of many different low-dimensional models and analytical techniques, including sparse and low-rank models, and both convex and non-convex formulations. Readers will learn how to develop efficient and scalable algorithms for solving real-world problems, supported by numerous examples and exercises throughout, and how to use the computational tools learnt in several application contexts. Applications presented include scientific imaging, communication, face recognition, 3D vision, and deep networks for classification. With code available online, this is an ideal textbook for senior and graduate students in computer science, data science, and electrical engineering, as well as for those taking courses on sparsity, low-dimensional structures, and high-dimensional data. Foreword by Emmanuel Candès.

Foreword
Preface
Acknowledgements
1. Introduction
Part I. Principles of Low-Dimensional Models: 2. Sparse Signal Models
3. Convex Methods for Sparse Signal Recovery
4. Convex Methods for Low-Rank Matrix Recovery
5. Decomposing Low-Rank and Sparse Matrices
6. Recovering General Low-Dimensional Models
7. Nonconvex Methods for Low-Dimensional Models
Part II. Computation for Large-Scale Problems: 8. Convex Optimization for Structured Signal Recovery
9. Nonconvex Optimization for High-Dimensional Problems
Part III. Applications to Real-World Problems: 10. Magnetic Resonance Imaging
11. Wideband Spectrum Sensing
12. Scientific Imaging Problems
13. Robust Face Recognition
14. Robust Photometric Stereo
15. Structured Texture Recovery
16. Deep Networks for Classification
Appendices: Appendix A. Facts from Linear Algebra and Matrix Analysis
Appendix B. Convex Sets and Functions
Appendix C. Optimization Problems and Optimality Conditions
Appendix D. Methods for Optimization
Appendix E. Facts from High-Dimensional Statistics
Bibliography
List of Symbols
Index.

Subject Areas: Signal processing [UYS], Machine learning [UYQM], Data analysis: general [GPH], Information theory [GPF]