Description
Springer Generalized Principal Component Analysis 2016 Edition by Rene Vidal Yi Ma Shankar Sastry
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.Rene 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.