  We address the problem of setting the kernel bandwidth used by Manifold
Learning algorithms to construct the graph Laplacian. Exploiting the connection
between manifold geometry, represented by the Riemannian metric, and the
Laplace-Beltrami operator, we set the bandwidth by optimizing the Laplacian's
ability to preserve the geometry of the data. Experiments show that this
principled approach is effective and robust.
