Nonlinear Dimensionality Reduction Frameworks. Rong Xu Chan su Lee. Outline. Intuition of Nonlinear Dimensionality Reduction(NLDR) ISOMAP LLE NLDR in Gait Analysis. Intuition: how does your brain store these pictures?. Brain Representation. Brain Representation. Every pixel?
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Chan su Lee
So, your brain successfully reduced the high-dimensional inputs to an intrinsically 3-dimensional manifold!
Discover low dimensional representations (smooth manifold) for data in high dimension.
Linear approaches(PCA, MDS) vs Non-linear approaches (ISOMAP, LLE)Manifold Learning
Constructing neighbourhood graph G for data in high dimension.
For each pair of points in G, Computing shortest path distances ---- geodesic distances.
Use Classical MDS with geodesic distances.
Euclidean distance Geodesic distanceNonlinear Approaches- ISOMAP
Josh. Tenenbaum, Vin de Silva, John langford 2000
K- nearest neighborhood (K=7)
DG is 1000 by 1000 (Euclidean) distance matrix of two neighbors (figure A)
Now DG is 1000 by 1000 geodesic distance matrix of two arbitrary points along the manifold(figure B)