@inbook{3789,
  title = {Discrete Regularization},
  booktitle = {Semi-supervised Learning},
  abstract = {Many real-world machine learning problems are situated on finite discrete sets,
  including dimensionality reduction, clustering, and transductive inference. A variety
  of approaches for learning from finite sets has been proposed from different
  motivations and for different problems. In most of those approaches, a finite set
  is modeled as a graph, in which the edges encode pairwise relationships among the
  objects in the set. Consequently many concepts and methods from graph theory are
  adopted. In particular, the graph Laplacian is widely used.
  In this chapter we present a systemic framework for learning from a finite set
  represented as a graph. We develop discrete analogues of a number of differential
  operators, and then construct a discrete analogue of classical regularization theory
  based on those discrete differential operators. The graph Laplacian based approaches
  are special cases of this general discrete regularization framework. An important
  thing implied in this framework is that we have a wide choices of regularization on
  graph in addition to the widely-used graph Laplacian based one.},
  pages = {237-250},
  series = {Adaptive computation and machine learning},
  editors = {O Chapelle and B Sch{\"o}lkopf and A Zien},
  publisher = {MIT Press},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Cambridge, MA, USA},
  month = nov,
  year = {2006},
  slug = {3789},
  author = {Zhou, D. and Sch{\"o}lkopf, B.},
  month_numeric = {11}
}