1. Non-linear Dimensionality Reduction by Locally Linear Inlaying Presented by Peng Zhang Tianjin University, China Yuexian Hou, Peng Zhang, Xiaowei Zhang, Xingxing Xu, & Wenjie Li

2. Why Nonlinear Methods  Inherent dimensionalities != the linear transformation of initial features Face image Example: Figures from ISOMAP paper L

3. Manifold Learning  Local Linearity  Global Embedding

4. A Run of ISOMAP L PCA ISOMAP Original

5. Another Run of ISOMAP Figures from ISOMAP paper

6. Other classical NLDR methods  LLE  LTSA  LLC  Laplacian Eigenmaps  LPP  ……

7. Drawbacks of these methods Most of these methods  at least quadratic time in N  fails on non-uniform dataset.  not robust to heterogeneous noise

8. Locally Linear Inlaying (LLI)  Linear time cost  Perform well on nonconvex samples  robust to heterogeneous noise

9. 1. Running time comparison

10. 2. Non-convex Swiss Roll Dataset L

11. 3. Swiss roll with heterogeneous noise Isomap LTSA LLC LLI Original 2-D projection

12. 4. “ Frey Face ” dataset Intensity of Illumination Pose

14. Connections to IR  LLI in text background? Positive  Linearity in local area is better than global data  Obtain local document sets (clusters or subtopics) Reasons for Negative  Different metric in text and imageDifferent metric  Image have natural manifold meaningmanifold meaning  LLI in Renaissance Project? Local context basis Global context-sensitive embedding

15. Thank You! Any Question???