2011

Geometric Structure of High-Dimensional Data and Dimensionality Reduction

Authors:

ISBN: 978-3-642-27496-1 (Print) 978-3-642-27497-8 (Online)

Table of contents (15 chapters)

  1. Front Matter

    Pages i-xix

  2. Introduction

    1. No Access

      Book Chapter

      Pages 1-26

      Introduction

  3. Data Geometry

    1. Front Matter

      Pages 27-27

    2. No Access

      Book Chapter

      Pages 29-49

      Preliminary Calculus on Manifolds

    3. No Access

      Book Chapter

      Pages 51-77

      Geometric Structure of High-Dimensional Data

    4. No Access

      Book Chapter

      Pages 79-91

      Data Models and Structures of Kernels of DR

  4. Linear Dimensionality Reduction

    1. Front Matter

      Pages 93-93

    2. No Access

      Book Chapter

      Pages 95-114

      Principal Component Analysis

    3. No Access

      Book Chapter

      Pages 115-129

      Classical Multidimensional Scaling

    4. No Access

      Book Chapter

      Pages 131-148

      Random Projection

  5. Nonlinear Dimensionality Reduction

    1. Front Matter

      Pages 149-149

    2. No Access

      Book Chapter

      Pages 151-180

      Isomaps

    3. No Access

      Book Chapter

      Pages 181-202

      Maximum Variance Unfolding

    4. No Access

      Book Chapter

      Pages 203-220

      Locally Linear Embedding

    5. No Access

      Book Chapter

      Pages 221-234

      Local Tangent Space Alignment

    6. No Access

      Book Chapter

      Pages 235-247

      Laplacian Eigenmaps

    7. No Access

      Book Chapter

      Pages 249-265

      Hessian Locally Linear Embedding

    8. No Access

      Book Chapter

      Pages 267-298

      Diffusion Maps

    9. No Access

      Book Chapter

      Pages 299-337

      Fast Algorithms for DR Approximation

  6. Back Matter

    Pages 339-356