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Titlebook: Generalized Principal Component Analysis; René Vidal,Yi Ma,S.S. Sastry Textbook 2016 Springer-Verlag New York 2016 Principal component ana

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发表于 2025-3-21 16:28:05 | 显示全部楼层 |阅读模式
书目名称Generalized Principal Component Analysis
编辑René Vidal,Yi Ma,S.S. Sastry
视频video
概述Introduces fundamental statistical, geometric and algebraic concepts.Encompasses relevant data clustering and modeling methods in machine learning.Addresses a general class of unsupervised learning pr
丛书名称Interdisciplinary Applied Mathematics
图书封面Titlebook: Generalized Principal Component Analysis;  René Vidal,Yi Ma,S.S. Sastry Textbook 2016 Springer-Verlag New York 2016 Principal component ana
描述.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 Dynam
出版日期Textbook 2016
关键词Principal component analysis; Robust principal component analysis; Manifold learning; Spectral clusteri
版次1
doihttps://doi.org/10.1007/978-0-387-87811-9
isbn_softcover978-1-4939-7912-7
isbn_ebook978-0-387-87811-9Series ISSN 0939-6047 Series E-ISSN 2196-9973
issn_series 0939-6047
copyrightSpringer-Verlag New York 2016
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发表于 2025-3-21 20:58:01 | 显示全部楼层
Statistical Methodsnd geometry of multiple subspaces, which leads to simple and elegant subspace clustering algorithms. However, while these methods can handle some noise in the data, they do not make explicit assumptions about the distribution of the noise or the data inside the subspaces. Therefore, the estimated su
发表于 2025-3-22 02:15:34 | 显示全部楼层
Spectral Methodsption that the data are not corrupted, we saw in Chapter 5 that algebraic-geometric methods are able to solve the subspace clustering problem in full generality, allowing for an arbitrary union of different subspaces of any dimensions and in any orientations, as long as sufficiently many data points
发表于 2025-3-22 06:52:47 | 显示全部楼层
Sparse and Low-Rank Methodsl methods for defining a subspace clustering affinity, and have noticed that we seem to be facing an important dilemma. On the one hand, local methods compute an affinity that depends only on the data points in a local neighborhood of each data point. Local methods can be rather efficient and somewh
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Hybrid System Identificationchanges of dynamics. For instance, the continuous trajectory of a bouncing ball results from alternating between free fall and elastic contact with the ground. However, hybrid systems can also be used to describe a complex process or time series that does not itself exhibit discontinuous behaviors,
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发表于 2025-3-23 04:39:34 | 显示全部楼层
0939-6047 endices 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 Dynam978-1-4939-7912-7978-0-387-87811-9Series ISSN 0939-6047 Series E-ISSN 2196-9973
发表于 2025-3-23 06:19:56 | 显示全部楼层
Sparse and Low-Rank Methodseoretical analysis that guarantees the correctness of clustering. Therefore, a natural question that arises is whether we can construct a subspace clustering affinity that utilizes global geometric relationships among all the data points, is computationally tractable when the dimension and number of
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