Title: Learning High Dimensional
Correspondences from Low Dimensional Manifolds
Abstract:
Different high dimensional data sets are often characterized by the same underlying
low dimensional manifold. For example, consider one data set of images that
consists of multiple views of object A, while another set consists of multiple
(and different) views of object B. In both cases, the variability arises from
the same underlying degrees of freedom—namely, camera position and orientation.
Given an image of object A, is it possible for a learning algorithm to
determine the corresponding view of object B?
We assume that the algorithm is given a small subset of images that are
in correspondence and a larger set of images that are not in correspondence. We
show how to solve this problem using two methods in dimensionality
reduction—the linear method of factor analysis (FA) and the nonlinear method of
locally linear embedding (LLE). Learning correspondences using FA is formulated
as a large missing data problem; using LLE, it is handled by incorporating
simple equality constraints into the quadratic optimization.
(Joint work with Ji Hun Ham and Daniel Lee)