Generalized Principal Component Analysis

  • René Vidal
  • Yi Ma
  • S.S. Sastry

Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 40)

Table of contents

  1. Front Matter
    Pages i-xxxii
  2. René Vidal, Yi Ma, S. Shankar Sastry
    Pages 1-21
  3. Modeling Data with a Single Subspace

    1. Front Matter
      Pages 23-23
    2. René Vidal, Yi Ma, S. Shankar Sastry
      Pages 25-62
    3. René Vidal, Yi Ma, S. Shankar Sastry
      Pages 63-122
    4. René Vidal, Yi Ma, S. Shankar Sastry
      Pages 123-168
  4. Modeling Data with Multiple Subspaces

    1. Front Matter
      Pages 169-169
    2. René Vidal, Yi Ma, S. Shankar Sastry
      Pages 171-215
    3. René Vidal, Yi Ma, S. Shankar Sastry
      Pages 217-266
    4. René Vidal, Yi Ma, S. Shankar Sastry
      Pages 267-289
    5. René Vidal, Yi Ma, S. Shankar Sastry
      Pages 291-346
  5. Applications

    1. Front Matter
      Pages 347-347
    2. René Vidal, Yi Ma, S. Shankar Sastry
      Pages 349-376
    3. René Vidal, Yi Ma, S. Shankar Sastry
      Pages 377-400
    4. René Vidal, Yi Ma, S. Shankar Sastry
      Pages 401-429
    5. René Vidal, Yi Ma, S. Shankar Sastry
      Pages 431-451
    6. René Vidal, Yi Ma, S. Shankar Sastry
      Pages 453-459
  6. Back Matter
    Pages 461-566

About this book

Introduction

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.

Keywords

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

Authors and affiliations

  • René Vidal
    • 1
  • Yi Ma
    • 2
  • S.S. Sastry
    • 3
  1. 1.Dept. of Biomed. Eng., Cntr for Imag. ScJohns Hopkins UniversityBALTIMOREUSA
  2. 2.URBANAUSA
  3. 3.Dept. of Elect. Eng. and Comp. Sc.University of California BerkeleyBERKELEYUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-87811-9
  • Copyright Information Springer-Verlag New York 2016
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-87810-2
  • Online ISBN 978-0-387-87811-9
  • Series Print ISSN 0939-6047
  • Series Online ISSN 2196-9973
  • About this book