Geometric Structure of High-Dimensional Data and Dimensionality Reduction

1. Introduction
Jianzhong Wang

Part I. Data Geometry

2. Preliminary Calculus on Manifolds
Jianzhong Wang

3. Geometric Structure of High-Dimensional Data
Jianzhong Wang

4. Data Models and Structures of Kernels of DR
Jianzhong Wang

Part II. Linear Dimensionality Reduction

5. Principal Component Analysis
Jianzhong Wang

6. Classical Multidimensional Scaling
Jianzhong Wang

7. Random Projection
Jianzhong Wang

Part III. Nonlinear Dimensionality Reduction

8. Isomaps
Jianzhong Wang

9. Maximum Variance Unfolding
Jianzhong Wang

10. Locally Linear Embedding
Jianzhong Wang

11. Local Tangent Space Alignment
Jianzhong Wang

12. Laplacian Eigenmaps
Jianzhong Wang

13. Hessian Locally Linear Embedding
Jianzhong Wang

14. Diffusion Maps
Jianzhong Wang

15. Fast Algorithms for DR Approximation
Jianzhong Wang

Keywords: Computer Science, Data Mining and Knowledge Discovery, Probability and Statistics in Computer Science, Applications of Mathematics, Data Structures, Cryptology and Information Theory