Editing Nonlinear dimensionality reduction (section)

=== Manifold sculpting ===

Manifold Sculpting<ref>Gashler, M. and Ventura, D. and Martinez, T., ''[http://axon.cs.byu.edu/papers/gashler2007nips.pdf Iterative Non-linear Dimensionality Reduction with Manifold Sculpting]'', In Platt, J.C. and Koller, D. and Singer, Y. and Roweis, S., editor, Advances in Neural Information Processing Systems 20, pp. 513–520, MIT Press, Cambridge, MA, 2008</ref> uses [[graduated optimization]] to find an embedding. Like other algorithms, it computes the ''k''-nearest neighbors and tries to seek an embedding that preserves relationships in local neighborhoods. It slowly scales variance out of higher dimensions, while simultaneously adjusting points in lower dimensions to preserve those relationships. If the rate of scaling is small, it can find very precise embeddings. It boasts higher empirical accuracy than other algorithms with several problems. It can also be used to refine the results from other manifold learning algorithms. It struggles to unfold some manifolds, however, unless a very slow scaling rate is used. It has no model.