Iterative Non-linear Dimensionality Reduction with Manifold Sculpting

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

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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.