Manifold Learning Theory and Applications (Hardcover)

Spectral Embedding Methods for Manifold Learning
Introduction
Spaces and Manifolds
Data on Manifolds
Linear Manifold Learning
Nonlinear Manifold Learning
Summary
Acknowledgment

Robust Laplacian Eigenmaps Using Global Information
Introduction
Graph Laplacian
Global Information of Manifold
Laplacian Eigenmaps with Global Information
Experiments
Summary
Bibliographical and Historical Remarks

Density Preserving Maps
Introduction
The Existence of Density Preserving Maps
Density Estimation on Submanifolds
Preserving the Estimated Density: The Optimization
Summary
Bibliographical and Historical Remarks

Sample Complexity in Manifold Learning
Introduction
Sample Complexity of Classification on a Manifold
Learning Smooth Class Boundaries
Sample Complexity of Testing the Manifold Hypothesis
Connections and Related Work
Sample Complexity of Empirical Risk Minimization
Relating Bounded Curvature to Covering Number
Class of Manifolds with a Bounded Covering Number
Fat-Shattering Dimension and Random Projections
Minimax Lower Bounds on the Sample Complexity
Algorithmic Implications
Summary

Manifold Alignment
Introduction
Formalization and Analysis
Variants of Manifold Alignment
Application Examples
Summary
Bibliographical and Historical Remarks
Acknowledgments

Large-scale Manifold Learning
Introduction
Background
Comparison of Sampling Methods
Large-Scale Manifold Learning
Summary
Bibliography and Historical Remarks

Metric and Heat Kernel
Introduction

Theoretic Background
Discrete Heat Kernel
Heat Kernel Simplification
Numerical Experiments
Applications
Summary
Bibliographical and Historical Remarks

Discrete Ricci Flow for Surface and 3-Manifold
Introduction
Theoretic Background
Surface Ricci Flow
3-Manifold Ricci Flow
Applications
Summary
Bibliographical and Historical Remarks

2D and 3D Objects Morphing Using Manifold Techniques
Introduction
Interpolation on Euclidean spaces
Generalization of Interpolation Algorithms on a Manifold M
Interpolation on SO(m)
Application: The Motion of a Rigid Object in Space
Interpolation on Shape Manifold
Examples of Fitting Curves on Shape Manifolds
Summary

Learning Image Manifolds from Local Features
Introduction
Joint Feature-Spatial Embedding
Solving the Out-Of-Sample Problem
From Feature Embedding to Image Embedding
Applications
Summary
Bibliographical and Historical remarks

Human Motion Analysis Applications of Manifold Learning
Introduction
Learning A Simple Motion Manifold
Factorized Generative Models
Generalized Style Factorization
Solving for Multiple Factors
Examples
Summary
Bibliographical and Historical remarks