  We present a method for finding high density, low-dimensional structures in
noisy point clouds. These structures are sets with zero Lebesgue measure with
respect to the $D$-dimensional ambient space and belong to a $d<D$ dimensional
space. We call them "singular features." Hunting for singular features
corresponds to finding unexpected or unknown structures hidden in point clouds
belonging to $\R^D$. Our method outputs well defined sets of dimensions $d<D$.
Unlike spectral clustering, the method works well in the presence of noise. We
show how to find singular features by first finding ridges in the estimated
density, followed by a filtering step based on the eigenvalues of the Hessian
of the density.
