Generalized Principal Component Analysis. 1st ed. 2016

種類:

電子ブック

責任表示:

by René Vidal, Yi Ma, Shankar Sastry

出版情報:

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

著者名:

• Vidal, René.
• Ma, Yi.
• Sastry, Shankar.
• SpringerLink (Online service)

シリーズ名:

Interdisciplinary Applied Mathematics ; 40

ISBN:

9780387878119 [0387878114]    

注記:

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.
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

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