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

Angle constrained path to cluster multiple manifolds