Robust manifold learning with CycleCut

Abstract

Many manifold learning algorithms utilise graphs of local neighbourhoods to estimate manifold topology. When neighbourhood 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 in unfolding manifolds with toroidal intrinsic variables without introducing significant distortions to local neighbourhoods. 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.

Keywords:

• neighbourhood graphs
• shortcut connection detection
• nonlinear dimensionality reduction
• manifold learning