Geometric Structure of High-Dimensional Data and Dimensionality Reduction

  • Jianzhong¬†Wang

Table of contents

  1. Front Matter
    Pages i-xix
  2. Introduction

    1. Jianzhong Wang
      Pages 1-26
  3. Data Geometry

    1. Front Matter
      Pages 27-27
    2. Jianzhong Wang
      Pages 29-49
    3. Jianzhong Wang
      Pages 79-91
  4. Linear Dimensionality Reduction

    1. Front Matter
      Pages 93-93
    2. Jianzhong Wang
      Pages 95-114
    3. Jianzhong Wang
      Pages 115-129
    4. Jianzhong Wang
      Pages 131-148
  5. Nonlinear Dimensionality Reduction

    1. Front Matter
      Pages 149-149
    2. Jianzhong Wang
      Pages 151-180
    3. Jianzhong Wang
      Pages 181-202
    4. Jianzhong Wang
      Pages 203-220
    5. Jianzhong Wang
      Pages 221-234
    6. Jianzhong Wang
      Pages 235-247
    7. Jianzhong Wang
      Pages 249-265
    8. Jianzhong Wang
      Pages 267-298
    9. Jianzhong Wang
      Pages 299-337
  6. Back Matter
    Pages 339-356

About this book

Introduction

"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.

Keywords

HEP dimensionality reduction geometric diffusion intrinsic dimensionality of data manifolds neighborhood in data randomization

Authors and affiliations

  • Jianzhong¬†Wang
    • 1
  1. 1.Department of Mathematics and StatisticsSam Houston State UniversityHuntsvilleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-27497-8
  • Copyright Information Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Computer Science
  • Print ISBN 978-3-642-27496-1
  • Online ISBN 978-3-642-27497-8
  • About this book