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COLT
2005
Springer

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

14 years 6 months ago
From Graphs to Manifolds - Weak and Strong Pointwise Consistency of Graph Laplacians
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 data-dependent weights to some weighted Laplace operator. Our investigation also includes the important case where the data lies on a submanifold of Rd .
Matthias Hein, Jean-Yves Audibert, Ulrike von Luxb
Added 26 Jun 2010
Updated 26 Jun 2010
Type Conference
Year 2005
Where COLT
Authors Matthias Hein, Jean-Yves Audibert, Ulrike von Luxburg
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