  We propose a spectral clustering method based on local principal components
analysis (PCA). After performing local PCA in selected neighborhoods, the
algorithm builds a nearest neighbor graph weighted according to a discrepancy
between the principal subspaces in the neighborhoods, and then applies spectral
clustering. As opposed to standard spectral methods based solely on pairwise
distances between points, our algorithm is able to resolve intersections. We
establish theoretical guarantees for simpler variants within a prototypical
mathematical framework for multi-manifold clustering, and evaluate our
algorithm on various simulated data sets.
