# Non-linear Dimensionality Reduction by Locally Linear Inlaying Presented by Peng Zhang Tianjin University, China Yuexian Hou, Peng Zhang, Xiaowei Zhang,

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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

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

Manifold Learning  Local Linearity  Global Embedding

A Run of ISOMAP L PCA ISOMAP Original

Another Run of ISOMAP Figures from ISOMAP paper

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

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

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

1. Running time comparison

2. Non-convex Swiss Roll Dataset L

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

4. “ Frey Face ” dataset Intensity of Illumination Pose

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

Thank You! Any Question???

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