| |
Abstract:
Drawing on the correspondence between the graph Laplacian, the
Laplace-Beltrami operator on a manifold, and the connections to
the heat equation, we propose a geometrically motivated algorithm
for constructing a representation for data sampled from a low
dimensional manifold embedded in a higher dimensional space. The
algorithm provides a computationally efficient approach to
nonlinear dimensionality reduction that has locality preserving
properties and a natural connection to clustering. Several
applications are considered.
|
