PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Uniform convergence of adaptive graph-based regularization
Matthias Hein
Proceedings of the 19th Annual Conference on Learning Theory pp. 50-64, 2006.

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.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:2563
Deposited By:Matthias Hein
Deposited On:22 November 2006