Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation

  author = {Chr.~Feuers\"anger and M.~Griebel},
  personid = {4},
  title = {Principal Manifold Learning by Sparse Grids},
  journal = {Computing},
  abstract = {In this paper, we deal with the construction of
		  lower-dimensional manifolds from high-dimensional data
		  which is an important task in data mining, machine learning
		  and statistics. Here, we consider principal manifolds as
		  the minimum of a regularized, non-linear empirical
		  quantization error functional. For the discretization we
		  use a sparse grid method in latent parameter space. This
		  approach avoids, to some extent, the curse of dimension of
		  conventional grids like in the GTM approach. The arising
		  non-linear problem is solved by a descent method which
		  resembles the expectation maximization algorithm. We
		  present our sparse grid principal manifold approach,
		  discuss its properties and report on the results of
		  numerical experiments for one-, two- and three-dimensional
		  model problems.},
  doi = {10.1007/s00607-009-0045-8},
  volume = {85},
  number = {4},
  year = {2009},
  http = {},
  pdf = { 1},
  note = {Also available as INS Preprint no 0801},
  inspreprintnum = {0801},
  annote = {inspreprint,article}