Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. From graphs to manifolds  weak and strong pointwise consistency of graph Laplacians
 Auer, P.: Learning theory. 18th Annual Conference on Learning Theory, COLT 2005 : Bertinoro, Italy, June 27  30, 2005; Proceedings Berlin: Springer, 2005 (Lecture Notes in Artificial Intelligence 3559) ISBN: 3540265562 ISBN: 9783540265566 pp.470485 
 Conference on Learning Theory (COLT) <18, 2005, Bertinoro/Italy> 

 English 
 Conference Paper 
 Fraunhofer IPSI; 2007 
Abstract
In the machine learning community it is generally believed that graph Laplacians corresponding to a finite sample of data points converge to a continuous Laplace operator if the sample size increases. Even though this assertion serves as a justification for many Laplacianbased algorithms, so far only some aspects of this claim have been rigorously proved. In this paper we close this gap by establishing the strong pointwise consistency of a family of graph Laplacians with datadependent weights to some weighted Laplace operator. Our investigation also includes the important case where the data lies on a submanifold of Rd.