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Conference Paper

Uniform Convergence of Adaptive Graph-Based Regularization

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons83958

Hein,  M
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Hein, M. (2006). Uniform Convergence of Adaptive Graph-Based Regularization. Learning Theory: 19th Annual Conference on Learning Theory (COLT 2006), 50-64.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-D05B-D
Abstract
The regularization functional induced by the graph Laplacian of a random neighborhood graph based on the data is adaptive in two ways. First it adapts to an underlying manifold structure and second to the density of the data-generating probability measure. We identify in this paper the limit of the regularizer and show uniform convergence over the space of Hoelder functions. As an intermediate step we derive upper bounds on the covering numbers of Hoelder functions on compact Riemannian manifolds, which are of independent interest for the theoretical analysis of manifold-based learning methods.