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.

• Type: Conference
• Year: 1997
• Where: NIPS
• Authors: Joshua B. Tenenbaum
• Keywords: Intrinsic Metric Structure, NIPS 1997, NIPS 2007, Nonlinear Dimensionality Reduction, Recoverlow-dimensional Nonlinear Structure