Generalized Principal Component Analysis

• Main Authors: Vidal, René (Author), Ma, Yi (Author), Sastry, S.S (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2016.
• Series: Interdisciplinary Applied Mathematics, 40
• Subjects: Mathematics.; Image processing.; Algebraic geometry.; System theory.; Statistics.; 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.

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 challen...

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.