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From Graphs to Manifolds Weak and Strong Pointwise Consistency of Graph Laplacians
 

Summary: From Graphs to Manifolds ­ Weak and Strong
Pointwise Consistency of Graph Laplacians
Matthias Hein1
, Jean-Yves Audibert2
, and Ulrike von Luxburg3
1
Max Planck Institute for Biological Cybernetics, T¨ubingen, Germany
2
CERTIS, ENPC, Paris, France
3
Fraunhofer IPSI, Darmstadt, Germany
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 Laplacian-
based algorithms, so far only some aspects of this claim have been rigor-
ously proved. In this paper we close this gap by establishing the strong
pointwise consistency of a family of graph Laplacians with data-
dependent weights to some weighted Laplace operator. Our investigation
also includes the important case where the data lies on a submanifold

  

Source: Audibert, Jean-Yves - Département d'Informatique, École Normale Supérieure

 

Collections: Computer Technologies and Information Sciences