Research Group of Prof. Dr. J. Garcke
Institute for Numerical Simulation

  author = {Jochen Garcke and Michael Griebel},
  title = {Semi-supervised learning with sparse grids},
  booktitle = {Proceedings of ICML, Workshop on Learning with Partially
		  Classified Training Data},
  year = {2005},
  editor = {Massih-Reza Amini and Olivier Chapelle and Rayid Ghani},
  pages = {19-28},
  abstract = {Sparse grids were recently introduced for classification
		  and regression problems. In this article we apply the
		  sparse grid approach to semi-supervised classification. We
		  formulate the semi-supervised learning problem by a
		  regularization approach. Here, besides a regression
		  formulation for the labeled data, an additional term is
		  involved which is based on the graph Laplacian for an
		  adjacency graph of all, labeled and unlabeled data points.
		  It reflects the intrinsic geometric structure of the data
		  distribution. We discretize the resulting problem in
		  function space by the sparse grid method and solve the
		  arising equations using the so-called combination
		  technique. In contrast to recently proposed kernel based
		  methods which currently scale cubic in regard to the number
		  of overall data, our method scales only linear, provided
		  that a sparse graph Laplacian is used. This allows to deal
		  with huge data sets which involve millions of points. We
		  show experimental results with the new approach.},
  annote = {other},
  file = {sgSemiSupICML.pdf:http\://},
  pdf = { 1}