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Interdisciplinary Applied Mathematics

Generalized Principal Component Analysis

Authors: Vidal, René, Ma, Yi, Sastry, S.S.

  • Addresses a general class of unsupervised learning problems
  • Encompasses relevant data clustering and modeling methods in machine learning
  • Introduces fundamental statistical, geometric and algebraic concepts
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eBook $69.99
price for USA (gross)
  • ISBN 978-0-387-87811-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA
  • ISBN 978-0-387-87810-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

About the authors

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.

Reviews

“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)


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Table of contents (13 chapters)

  • Introduction

    Vidal, René (et al.)

    Pages 1-21

  • Principal Component Analysis

    Vidal, René (et al.)

    Pages 25-62

  • Robust Principal Component Analysis

    Vidal, René (et al.)

    Pages 63-122

  • Nonlinear and Nonparametric Extensions

    Vidal, René (et al.)

    Pages 123-168

  • Algebraic-Geometric Methods

    Vidal, René (et al.)

    Pages 171-215

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-0-387-87811-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA
  • ISBN 978-0-387-87810-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Generalized Principal Component Analysis
Authors
Series Title
Interdisciplinary Applied Mathematics
Series Volume
40
Copyright
2016
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-87811-9
DOI
10.1007/978-0-387-87811-9
Hardcover ISBN
978-0-387-87810-2
Series ISSN
0939-6047
Edition Number
1
Number of Pages
XXXII, 566
Number of Illustrations and Tables
38 b/w illustrations, 83 illustrations in colour
Topics