René Vidal, Yi Ma, S. Shankar Sastry.
Generalized Principal Component Analysis.
Springer. 2016
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.