Mapping a Manifold of Perceptual Observations

Abstract

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 feature mapping procedure, or isomap, is able to reliably recover low-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. 1 Introduction In psychological or computational research on perceptual categorization, it is generally taken for granted t...