Name
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 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 ${\mathbb R}^{d}$. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1007/11503415_32 | COLT |
Keywords | Field | DocType |
strong pointwise consistency,sample size increase,dependent weight,laplacian-based algorithm,graph laplacians,important case,data point,finite sample,weighted laplace operator,continuous laplace operator,mathbb r,graph laplacian,machine learning,sample size,laplace operator | Data point,Discrete mathematics,Assertion,Differential operator,Submanifold,Manifold,Sample size determination,Mathematics,Pointwise,Laplace operator | Conference |
Volume | ISSN | ISBN |
3559 | 0302-9743 | 3-540-26556-2 |
Citations | PageRank | References |
81 | 10.96 | 2 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Matthias Hein | 1 | 663 | 62.80 |
| Jean-yves Audibert | 2 | 1225 | 78.45 |
| von luxburg | 3 | 3246 | 170.11 |