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Titlebook: Geometric Structure of High-Dimensional Data and Dimensionality Reduction; Jianzhong Wang Book 2012 Higher Education Press, Beijing and Sp

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发表于 2025-3-21 17:58:24 | 显示全部楼层 |阅读模式
书目名称Geometric Structure of High-Dimensional Data and Dimensionality Reduction
编辑Jianzhong Wang
视频videohttp://file.papertrans.cn/384/383612/383612.mp4
概述Comprehensively introducing all of popular linear and nonlinear dimensionality reduction methods.Full description of mathematical and statistical foundations of the introduced dimensionality reduction
图书封面Titlebook: Geometric Structure of High-Dimensional Data and Dimensionality Reduction;  Jianzhong Wang Book 2012 Higher Education Press, Beijing and Sp
描述."Geometric Structure of High-Dimensional Data and Dimensionality Reduction" adopts data geometry as a framework to address various methods of dimensionality reduction. In addition to the introduction to well-known linear methods, the book moreover stresses the recently developed nonlinear methods and introduces the applications of dimensionality reduction in many areas, such as face recognition, image segmentation, data classification, data visualization, and hyperspectral imagery data analysis. Numerous tables and graphs are included to illustrate the ideas, effects, and shortcomings of the methods. MATLAB code of all dimensionality reduction algorithms is provided to aid the readers with the implementations on computers. .The book will be useful for mathematicians, statisticians, computer scientists, and data analysts. It is also a valuable handbook for other practitioners who have a basic background in mathematics, statistics and/or computer algorithms, like internet search engine designers, physicists, geologists, electronic engineers, and economists..Jianzhong Wang is a Professor of Mathematics at Sam Houston State University, U.S.A..
出版日期Book 2012
关键词HEP; dimensionality reduction; geometric diffusion; intrinsic dimensionality of data; manifolds; neighbor
版次1
doihttps://doi.org/10.1007/978-3-642-27497-8
isbn_ebook978-3-642-27497-8
copyrightHigher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2012
The information of publication is updating

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Geometric Structure of High-Dimensional Data and Dimensionality Reduction
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Geometric Structure of High-Dimensional Data system on a data set defines a data graph, which can be considered as a discrete form of a manifold. In Section 2, we introduce the basic concepts of graphs. In Section 3, the spectral graph analysis is introduced as a tool for analyzing the data geometry. Particularly, the Laplacian on a graph is
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Local Tangent Space Alignmentensional representation of the patch. An alignment technique is introduced in LTSA to align the local representation to a global one. The chapter is organized as follows. In Section 11.1, we describe the method, paying more attention to the global alignment technique. In Section 11.2, the LTSA algor
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