Mapping a Manifold of Perceptual Observations

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Mapping a Manifold of Perceptual Observations
Nonlinear dimensionality reduction is formulated here as the problem of trying to find a Euclidean feature-space embedding of a set of observations that preserves as closely as possibletheir intrinsic metric structure – the distancesbetween points on the observation manifold as measured along geodesic paths. Our isometric featuremapping procedure, or isomap, is able to reliably recoverlow-dimensional nonlinear structure in realistic perceptual data sets, such as a manifold of face images, where conventional global mapping methods find only local minima. The recovered map provides a canonical set of globally meaningful features, which allows perceptual transformations such as interpolation, extrapolation, and analogy – highly nonlinear transformations in the original observation space – to be computed with simple linear operations in feature space.
Joshua B. Tenenbaum
Added 01 Nov 2010
Updated 01 Nov 2010
Type Conference
Year 1997
Where NIPS
Authors Joshua B. Tenenbaum
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