Geometric structure of high-dimensional data and dimensionality reduction

著者

    • Wang, Jianzhong

書誌事項

Geometric structure of high-dimensional data and dimensionality reduction

Jianzhong Wang

Higher Education Press, 2012 , Springer, 2012

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注記

Includes bibliographical references and index

収録内容

  • Pt. 1. Data geometry
  • pt. 2. Linear dimensionality reduction
  • pt. 3. Nonlinear dimensionality reduction
  • 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
  • Appendix A. Differential forms and operators on manifolds
  • Index

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