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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 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

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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

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

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ISOMAP Result

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LLE vs. ISOMAP Residual Variance vs. Dimesionality of ISOMAPResidual Variance vs. Dimesionality of LLE