# Learning the
Density Structure of High-Dimensional Data

## Yoshua Bengio

We claim and present arguments to the effect that a large class
of manifold learning algorithms that are essentially local
will suffer from at least four generic problems associated
with noise in the data, curvature of the manifold, dimensionality
of the manifold, and the presence of many manifolds with
little data per manifold. This suggests non-local manifold
learning algorithms which attempt to discover shared structure
in the tangent planes at different positions. A criterion
for such an algorithm is proposed and experiments estimating
a tangent plane prediction function are presented, showing
its advantages with respect to local manifold learning
algorithms.