Generalized Principal Component Analysis

by René Vidal, Yi Ma, Shankar Sastry

Overview

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.

Product Details

ISBN-13:	9780387878102
Publisher:	Springer New York
Publication date:	04/12/2016
Series:	Interdisciplinary Applied Mathematics , #40
Edition description:	1st ed. 2016
Pages:	566
Product dimensions:	9.30(w) x 6.30(h) x 1.50(d)

About the Author

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.

Table of Contents

Preface.- Acknowledgments.- Glossary of Notation.- Introduction.- I Modeling Data with Single Subspace.- Principal Component Analysis.- Robust Principal Component Analysis.- Nonlinear and Nonparametric Extensions.- II Modeling Data with Multiple Subspaces.- Algebraic-Geometric Methods.- Statistical Methods.- Spectral Methods.- Sparse and Low-Rank Methods.- III Applications.- Image Representation.- Image Segmentation.- Motion Segmentation.- Hybrid System Identification.- Final Words.- Appendices.- References.- Index.

Editorial 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)

From the Publisher