From Graphs to Manifolds - Weak and Strong Pointwise Consistency of Graph Laplacians
2005
Conference Paper
ei
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 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 $R^d$.
Author(s): | Hein, M. and Audibert, J. and von Luxburg, U. |
Journal: | Proceedings of the 18th Conference on Learning Theory (COLT) |
Pages: | 470-485 |
Year: | 2005 |
Day: | 0 |
Department(s): | Empirical Inference |
Bibtex Type: | Conference Paper (inproceedings) |
Event Name: | Conference on Learning Theory |
Digital: | 0 |
Note: | Student Paper Award |
Organization: | Max-Planck-Gesellschaft |
School: | Biologische Kybernetik |
Links: |
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BibTex @inproceedings{3213, title = {From Graphs to Manifolds - Weak and Strong Pointwise Consistency of Graph Laplacians}, author = {Hein, M. and Audibert, J. and von Luxburg, U.}, journal = {Proceedings of the 18th Conference on Learning Theory (COLT)}, pages = {470-485}, organization = {Max-Planck-Gesellschaft}, school = {Biologische Kybernetik}, year = {2005}, note = {Student Paper Award}, doi = {} } |