Finding Singular Features
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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 ^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.
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