  In this paper, we propose a method to cluster multiple intersected manifolds.
The algorithm chooses several landmark nodes randomly and then checks whether
there is an angle constrained path between each landmark node and every other
node in the neighborhood graph. When the points lie on different manifolds with
intersection they should not be connected using a smooth path, thus the angle
constraint is used to prevent connecting points from one cluster to another
one. The resulting algorithm is implemented as a simple variation of Dijkstras
algorithm used in Isomap. However, Isomap was specifically designed for
dimensionality reduction in the single-manifold setting, and in particular,
can-not handle intersections. Our method is simpler than the previous proposals
in the literature and performs comparably to the best methods, both on
simulated and some real datasets.
