Part of Advances in Neural Information Processing Systems 20 (NIPS 2007)
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.