Overview
- Introduces fundamental statistical, geometric and algebraic concepts
- Encompasses relevant data clustering and modeling methods in machine learning
- Addresses a general class of unsupervised learning problems
- Generalizes the theory and methods of principal component anaylsis to the cases when the data can be severely contaminated with errors and outliers as well as when the data may contain more than one low-dimensional subspace
Part of the book series: Interdisciplinary Applied Mathematics (IAM, volume 40)
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About this book
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.Similar content being viewed by others
Keywords
Table of contents (13 chapters)
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Front Matter
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Modeling Data with a Single Subspace
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Front Matter
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Modeling Data with Multiple Subspaces
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Front Matter
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Applications
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Front Matter
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Back Matter
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)
Authors and Affiliations
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.
Bibliographic Information
Book Title: Generalized Principal Component Analysis
Authors: René Vidal, Yi Ma, S.S. Sastry
Series Title: Interdisciplinary Applied Mathematics
DOI: https://doi.org/10.1007/978-0-387-87811-9
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 2016
Hardcover ISBN: 978-0-387-87810-2Published: 12 April 2016
Softcover ISBN: 978-1-4939-7912-7Published: 14 April 2018
eBook ISBN: 978-0-387-87811-9Published: 11 April 2016
Series ISSN: 0939-6047
Series E-ISSN: 2196-9973
Edition Number: 1
Number of Pages: XXXII, 566
Number of Illustrations: 38 b/w illustrations, 83 illustrations in colour
Topics: Systems Theory, Control, Image Processing and Computer Vision, Signal, Image and Speech Processing, Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences, Algebraic Geometry