| Description |
1 online resource (xviii, 356 pages) : illustrations |
| Contents |
Part 1. Introduction -- Introduction -- Part I. Data Geometry -- Preliminary Calculus on Manifolds -- Geometric Structure of High-Dimensional Data -- Data Models and Structures of Kernels of DR -- Part II. Linear Dimensionality Reduction -- Principal Component Analysis -- Classical Multidimensional Scaling -- Random Projection -- Part III. Nonlinear Dimensionality Reduction -- Isomaps -- Maximum Variance Unfolding -- Locally Linear Embedding -- Local Tangent Space Alignment -- Laplacian Eigenmaps -- Hessian Locally Linear Embedding -- Diffusion Maps -- Fast Algorithms for DR Approximation |
| Summary |
Annotation "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 |
| Analysis |
Computer science |
|
Data structures (Computer science) |
|
Data mining |
|
Mathematics |
|
Probability and Statistics in Computer Science |
|
Applications of Mathematics |
|
Data Structures, Cryptology and Information Theory |
| Bibliography |
Includes bibliographical references and index |
| Subject |
Data structures (Computer science)
|
|
COMPUTERS -- Data Processing.
|
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Informatique.
|
|
Data structures (Computer science)
|
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Hochdimensionale Daten
|
|
Dimensionsreduktion
|
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Geometrische Methode
|
| Form |
Electronic book
|
| ISBN |
9783642274978 |
|
3642274978 |
|
7040317044 |
|
9787040317046 |
|
364227496X |
|
9783642274961 |
|
