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Regularization on Discrete Spaces

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons84330

Zhou,  D
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84193

Schölkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Zitation

Zhou, D., & Schölkopf, B. (2005). Regularization on Discrete Spaces. Pattern Recognition, Proceedings of the 27th DAGM Symposium, 361-368.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0013-D4C7-A
Zusammenfassung
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.