Robust manifold learning with CycleCut

Many manifold learning algorithms utilize graphs of local neighborhoods to estimate manifold topology. When neighborhood connections short-circuit between geodesically distant regions of the manifold, poor results are obtained due to the compromises that the manifold learner must make to satisfy the erroneous criteria. Also, existing manifold learning algorithms have difficulty unfolding manifolds with toroidal intrinsic variables without introducing significant distortions to local neighborhoods. An algorithm called CycleCut is presented which prepares data for manifold learning by removing short-circuit connections, and by severing toroidal connections in a manifold.