LLE and ISOMAP Analysis of Robot Images

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LLE and ISOMAP Analysis of Robot Images

• Rong Xu

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Background

• Intuition of Dimensionality Reduction
• Linear Approach
• PCA(Principal Component Analysis)

• Nonlinear Approach
• ISOMAP(ISOmetric MAPping)
• LLE(Locally Linear Embedding)
• Motivations of NLDR analysis of Robot Images
• Learning the image representation of embedding
  space.
• Finding out the mapping.
• Reinforcement learning of embedding space.

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ISOMAP
Josh. Tenenbaum, Vin de Silva, John langford 2000

• Constructing neighbourhood graph G
• For each pair of points in G, Computing shortest
  path distances ---- geodesic distances.
• Use Classical MDS with geodesic distances.

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LLE(Locally Linear Embedding)
Lawrence K. Saul Sam T. Roweis

• Find K nearest neighbors per data point
• Compute the weights Wij that best reconstruct
  each data point from its neighbors
• Compute the vectors best reconstructed by the
  weights Wij,

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LLE Result
283 images taken during a full sweep of a robot
dogs head.
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ISOMAP Result
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LLE vs. ISOMAP

• Residual Variance vs. Dimesionality of ISOMAP

Residual Variance vs. Dimesionality of LLE