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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
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Manifold Learning Local Linearity Global Embedding
MnR
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A Run of ISOMAP
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PCA ISOMAPOriginal
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
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3. Swiss roll with heterogeneous noise
Isomap
LTSA LLC LLI
Original 2-D projection
4. “Frey Face” dataset
Intensity of Illumination
Pose
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convert
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Transformation
Embedding
Translation
Rotation , Scaling,Mirror Projection
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???
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