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

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Manifold Learning Local Linearity Global Embedding

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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

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3. Swiss roll with heterogeneous noise

Isomap

LTSA LLC LLI

Original 2-D projection

4. “Frey Face” dataset

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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 image Image have natural manifold meaning

LLI in Renaissance Project? Local context basis Global context-sensitive embedding

Thank You!

Any Question???