High-Dimensional Data Analysis with Low-Dimensional Models

✍ Scribed by John Wright, Yi Ma

• Publisher: Cambridge University Press
• Year: 2022
• Tongue: English
• Leaves: 730
• Category: Library

✦ Synopsis

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.

Bridges the gap between principles and applications of low-dimensional models for high-dimensional data analysis
Covers a wide range of application areas
Accompanied online by code
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.