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.
Slide 3
ISOMAP Constructing neighbourhood graph G For each pair of
points in G, Computing shortest path distances ---- geodesic
distances. Use Classical MDS with geodesic distances. Josh.
Tenenbaum, Vin de Silva, John langford 2000
Slide 4
LLE(Locally Linear Embedding) Find K nearest neighbors per data
point Compute the weights W ij that best reconstruct each data
point from its neighbors Compute the vectors best reconstructed by
the weights W ij, Lawrence K. Saul & Sam T. Roweis
Slide 5
283 images taken during a full sweep of a robot dogs head. LLE
Result
Slide 6
ISOMAP Result
Slide 7
LLE vs. ISOMAP Residual Variance vs. Dimesionality of
ISOMAPResidual Variance vs. Dimesionality of LLE