From graphs to manifolds - Weak and strong pointwise consistency of graph Laplacians
From graphs to manifolds - Weak and strong pointwise consistency of graph Laplacians
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DOI：
10.1007/11503415_32
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发表时间：
2005-01-01
期刊：
影响因子：
--
通讯作者：
von Luxburg, U
中科院分区：
文献类型：
--
作者：
Hein, M;Audibert, JY;von Luxburg, U
在机器学习领域，通常认为，如果样本大小增加，则对应于数据点的有限样本的图拉普拉斯算子收敛到连续的拉普拉斯算子。尽管这一断言可以作为许多基于拉普拉斯算子的算法的理由，但到目前为止，这一断言的某些方面仅得到了严格的证明。在本文中，我们关闭这个差距，建立强点态一致性的一个家庭的图Laplacian与数据依赖的重量，一些加权拉普拉斯运营商。我们的研究还包括重要的情况下，数据位于一个子流形的R-d。
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.