Michael Gashler, Dan Ventura, Tony Martinez
Many algorithms have been recently developed for reducing dimensionality by projecting data onto an intrinsic non-linear manifold. Unfortunately, existing algo- rithms often lose signiﬁcant precision in this transformation. Manifold Sculpting is a new algorithm that iteratively reduces dimensionality by simulating surface tension in local neighborhoods. We present several experiments that show Man- ifold Sculpting yields more accurate results than existing algorithms with both generated and natural data-sets. Manifold Sculpting is also able to beneﬁt from both prior dimensionality reduction efforts.