05374nam 22008415 450 991025407100332120200702180943.00-387-87811-410.1007/978-0-387-87811-9(CKB)3710000000653196(SSID)ssj0001665965(PQKBManifestationID)16455443(PQKBTitleCode)TC0001665965(PQKBWorkID)15000762(PQKB)11235445(DE-He213)978-0-387-87811-9(MiAaPQ)EBC6313098(MiAaPQ)EBC5584556(Au-PeEL)EBL5584556(OCoLC)946944433(PPN)193442361(EXLCZ)99371000000065319620160411d2016 u| 0engurnn|008mamaatxtccrGeneralized Principal Component Analysis /by René Vidal, Yi Ma, Shankar Sastry1st ed. 2016.New York, NY :Springer New York :Imprint: Springer,2016.1 online resource (XXXII, 566 p. 121 illus., 83 illus. in color.) Interdisciplinary Applied Mathematics,0939-6047 ;40Bibliographic Level Mode of Issuance: Monograph0-387-87810-6 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 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.Interdisciplinary Applied Mathematics,0939-6047 ;40System theoryOptical data processingSignal processingImage processingSpeech processing systemsStatistics Algebraic geometrySystems Theory, Controlhttps://scigraph.springernature.com/ontologies/product-market-codes/M13070Image Processing and Computer Visionhttps://scigraph.springernature.com/ontologies/product-market-codes/I22021Signal, Image and Speech Processinghttps://scigraph.springernature.com/ontologies/product-market-codes/T24051Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Scienceshttps://scigraph.springernature.com/ontologies/product-market-codes/S17020Algebraic Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11019System theory.Optical data processing.Signal processing.Image processing.Speech processing systems.Statistics .Algebraic geometry.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.519.5354Vidal Renéauthttp://id.loc.gov/vocabulary/relators/aut755927Ma Yiauthttp://id.loc.gov/vocabulary/relators/autSastry Shankarauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910254071003321Generalized Principal Component Analysis2283989UNINA