Generalized Principal Component Analysis

1. Front Matter

   Pages i-xxxii

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2. Introduction

   • René Vidal, Yi Ma, S. Shankar Sastry

   Pages 1-21

3. Modeling Data with a Single Subspace

   1. Front Matter

      Pages 23-23

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   2. Principal Component Analysis

      • René Vidal, Yi Ma, S. Shankar Sastry

      Pages 25-62

   3. Robust Principal Component Analysis

      • René Vidal, Yi Ma, S. Shankar Sastry

      Pages 63-122

   4. Nonlinear and Nonparametric Extensions

      • René Vidal, Yi Ma, S. Shankar Sastry

      Pages 123-168

4. Modeling Data with Multiple Subspaces

   1. Front Matter

      Pages 169-169

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   2. Algebraic-Geometric Methods

      • René Vidal, Yi Ma, S. Shankar Sastry

      Pages 171-215

   3. Statistical Methods

      • René Vidal, Yi Ma, S. Shankar Sastry

      Pages 217-266

   4. Spectral Methods

      • René Vidal, Yi Ma, S. Shankar Sastry

      Pages 267-289

   5. Sparse and Low-Rank Methods

      • René Vidal, Yi Ma, S. Shankar Sastry

      Pages 291-346

5. Applications

   1. Front Matter

      Pages 347-347

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   2. Image Representation

      • René Vidal, Yi Ma, S. Shankar Sastry

      Pages 349-376

   3. Image Segmentation

      • René Vidal, Yi Ma, S. Shankar Sastry

      Pages 377-400

   4. Motion Segmentation

      • René Vidal, Yi Ma, S. Shankar Sastry

      Pages 401-429

   5. Hybrid System Identification

      • René Vidal, Yi Ma, S. Shankar Sastry

      Pages 431-451

   6. Final Words

      • René Vidal, Yi Ma, S. Shankar Sastry

      Pages 453-459

6. Back Matter

   Pages 461-566

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This book provides a comprehensive introduction to the latest advances in the mathematical theory and computational tools for modeling high-dimensional data drawn from one or multiple low-dimensional subspaces (or manifolds) and potentially corrupted by noise, gross errors, or outliers. This challenging task requires the development of new algebraic, geometric, statistical, and computational methods for efficient and robust estimation and segmentation of one or multiple subspaces. The book also presents interesting real-world applications of these new methods in image processing, image and video segmentation, face recognition and clustering, and hybrid system identification etc.

This book is intended to serve as a textbook for graduate students and beginning researchers in data science, machine learning, computer vision, image and signal processing, and systems theory. It contains ample illustrations, examples, and exercises and is made largely self-contained with three Appendices which survey basic concepts and principles from statistics, optimization, and algebraic-geometry used in this book.

René Vidal is a Professor of Biomedical Engineering and Director of the Vision Dynamics and Learning Lab at The Johns Hopkins University. 

Yi Ma is Executive Dean and Professor at the School of Information Science and Technology at ShanghaiTech University. S. Shankar Sastry is Dean of the College of Engineering, Professor of Electrical Engineering and Computer Science and Professor of Bioengineering at the University of California, Berkeley.

• Principal component analysis
• Robust principal component analysis
• Manifold learning
• Spectral clustering
• Subspace clustering
• Subspace arrangements
• Sparse representation theory
• Image and video segmentation
• Hybrid system identification
• Low-rank matrix theory
• Linear subspace models

“The book under review provides a timely and comprehensive description of the classic and modern PCA-based and other dimension reduction techniques. Although the topic of dimension reduction has been briefly converted in quite a few books and review papers, this book should be especially applauded for its unique depth and comprehensiveness. … Overall, this is one of the best books on PCA and modern dimension reduction techniques and should expect an increasing popularity.” (Steven (Shuangge) Ma, Mathematical Reviews, January, 2017)

• Dept. of Biomed. Eng., Cntr for Imag. Sc, Johns Hopkins University, BALTIMORE, USA

  René Vidal

• URBANA, USA

  Yi Ma

• Dept. of Elect. Eng. and Comp. Sc., University of California Berkeley, BERKELEY, USA

  S.S. Sastry

René Vidal is a Professor of Biomedical Engineering and Director of the Vision Dynamics and Learning Lab at The Johns Hopkins University.

Yi Ma is Executive Dean and Professor at the School of Information Science and Technology at ShanghaiTech University.

S. Shankar Sastry is Dean of the College of Engineering, Professor of Electrical Engineering and Computer Science and Professor of Bioengineering at the University of California, Berkeley.

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