Geometric structure of high-dimensional data and dimensionality reduction
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Bibliographic Information
Geometric structure of high-dimensional data and dimensionality reduction
Higher Education Press, 2012 , Springer, 2012
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Note
Includes bibliographical references and index
Contents of Works
- 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