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

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.

Table of Contents:
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.

About the Author :
John Wright is an Associate Professor in the Electrical Engineering Department and the Data Science Institute at Columbia University. Yi Ma is a Professor in the Department of Electrical Engineering and Computer Sciences at the University of California, Berkeley. He is a Fellow of the IEEE, ACM, and SIAM.

Review :
'Students will learn a lot from reading this book … They will learn about mathematical reasoning, they will learn about data models and about connecting those to reality, and they will learn about algorithms. The book also contains computer scripts so that we can see ideas in action, and carefully crafted exercises making it perfect for upper-level undergraduate or graduate-level instruction. The breadth and depth make this a reference for anyone interested in the mathematical foundations of data science.' Emmanuel Candès, Stanford University (from the foreword) '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