Header logo is

Regularization on Discrete Spaces

2005

Conference Paper

ei


We consider the classification problem on a finite set of objects. Some of them are labeled, and the task is to predict the labels of the remaining unlabeled ones. Such an estimation problem is generally referred to as transductive inference. It is well-known that many meaningful inductive or supervised methods can be derived from a regularization framework, which minimizes a loss function plus a regularization term. In the same spirit, we propose a general discrete regularization framework defined on finite object sets, which can be thought of as the discrete analogue of classical regularization theory. A family of transductive inference schemes is then systemically derived from the framework, including our earlier algorithm for transductive inference, with which we obtained encouraging results on many practical classification problems. The discrete regularization framework is built on the discrete analysis and geometry developed by ourselves, in which a number of discrete differential operators of various orders are constructed, which can be thought of as the discrete analogue of their counterparts in the continuous case.

Author(s): Zhou, D. and Schölkopf, B.
Book Title: Pattern Recognition, Lecture Notes in Computer Science, Vol. 3663
Journal: Pattern Recognition, Proceedings of the 27th DAGM Symposium
Pages: 361-368
Year: 2005
Month: August
Day: 0
Editors: WG Kropatsch and R Sablatnig and A Hanbury
Publisher: Springer

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

DOI: 10.1007/11550518_45
Event Name: 27th DAGM Symposium
Event Place: Vienna, Austria

Address: Berlin, Germany
Digital: 0
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF
PostScript

BibTex

@inproceedings{3209,
  title = {Regularization on Discrete Spaces},
  author = {Zhou, D. and Sch{\"o}lkopf, B.},
  journal = {Pattern Recognition, Proceedings of the 27th DAGM Symposium},
  booktitle = {Pattern Recognition, Lecture Notes in Computer Science, Vol. 3663},
  pages = {361-368},
  editors = {WG Kropatsch and R Sablatnig and A Hanbury},
  publisher = {Springer},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Berlin, Germany},
  month = aug,
  year = {2005},
  month_numeric = {8}
}