Generalized Principal Component Analysis / by René Vidal, Yi Ma, Shankar Sastry.

Format:

Book

Author/Creator:

Vidal, René, Author.

Ma, Yi, Author.

Sastry, Shankar, Author.

Series:

Interdisciplinary Applied Mathematics, 0939-6047 ; 40

Language:

English

Subjects (All):

System theory.

Optical data processing.

Signal processing.

Image processing.

Speech processing systems.

Statistics.

Geometry, Algebraic.

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.

Local Subjects:

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.

Physical Description:

1 online resource (XXXII, 566 p. 121 illus., 83 illus. in color.)

Edition:

1st ed. 2016.

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 2016.

Language Note:

English

Summary:

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.

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.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Description based on publisher supplied metadata and other sources.

ISBN:

0-387-87811-4

OCLC:

946944433