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Discrete Regularization

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

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

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Citation

Zhou, D., & Schölkopf, B. (2006). Discrete Regularization. In O. Chapelle, B. Schölkopf, & A. Zien (Eds.), Semi-Supervised Learning (pp. 237-250). Cambridge, MA, USA: MIT Press.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-CF91-9
Abstract
This chapter presents a systemic framework for learning from a finite set represented as a graph. Discrete analogues are developed here of a number of differential operators, and then a discrete analogue of classical regularization theory is constructed based on those discrete differential operators. The graph Laplacian-based approaches are special cases of this general discrete regularization framework. More importantly, new approaches based on other different differential operators are derived as well. 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 applied, in particular, graph Laplacians.