Geometric Structure of High-Dimensional Data and Dimensionality Reduction

Přední strana obálky
Springer Science & Business Media, 28. 4. 2012 - Počet stran: 356

"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.

 

Vybrané stránky

Obsah

Chapter 1 Introduction
1
Part I Data Geometry
27
Chapter 2 Preliminary Calculus on Manifolds
28
Chapter 3 Geometric Structure of HighDimensional Data
51
Chapter 4 Data Models and Structures ofKernels of DR
78
Part II Linear DimensionalityReduction
92
Chapter 5 Principal Component Analysis
93
Chapter 6 Classical Multidimensional Scaling
115
Chapter 9 Maximum Variance Unfolding
181
Chapter 10 Locally Linear Embedding
203
Chapter 11 Local Tangent Space Alignment
221
Chapter 12 Laplacian Eigenmaps
235
Chapter 13 Hessian Locally Linear Embedding
249
Chapter 14 Diffusion Maps
266
Chapter 15 Fast Algorithms for DR Approximation
299
Appendix A Differential Forms and Operators on Manifolds
339

Chapter 7 Random Projection
131
Part III Nonlinear Dimensionality Reduction
149
Chapter 8 Isomaps
150
Index
348
Autorská práva

Další vydání - Zobrazit všechny

Geometric Structure of High-Dimensional Data and Dimensionality Reduction
Jianzhong Wang
Náhled není k dispozici. - 2012
Geometric Structure of High-Dimensional Data and Dimensionality Reduction
Jianzhong Wang
Náhled není k dispozici. - 2015

Běžně se vyskytující výrazy a sousloví

3D-cluster adjacency matrix applied Assume called CMDS columns compute constraint construct d-dimensional data graph data matrix defined denote diffusion maps digraph Dmaps DR data set DR kernel DR methods DR results eigen Eigen decomposition eigenfaces eigenfunction eigenvalue eigenvectors Euclidean distance matrix Euclidean metric face recognition FAT algorithms feature Gaussian geodesic distance geometry GL-Dmaps Gram matrix graph distance graph G Hence Hessian functional high-dimensional data input intrinsic dimension isfield isfield options Isomap Isomap algorithm Laplacian eigenmaps Lemma locally linear embedding low-dimensional LTSA manifold neighborhood system neighbors Node noise nonlinear dimensionality reduction nonlinear DR obtained output points PRAT principal components problem Punched sphere random matrix random projection random vector rank-revealing S-curve sampled Section semidefinite programming similarity similarity matrix singular value sparse spectral decomposition standard Isomap Step subspace surfaces Swiss roll symmetric tangent space Theorem weight matrix

Bibliografické údaje

NázevGeometric Structure of High-Dimensional Data and Dimensionality Reduction
AutorJianzhong Wang
Vydáníilustrované vydání
VydavatelSpringer Science & Business Media, 2012
ISBN3642274978, 9783642274978
DélkaPočet stran: 356
  
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