Bi-stochastically normalized graph Laplacian: convergence to manifold Laplacian and robustness to outlier noise. (arXiv:2206.11386v1 [math.ST])

Web: http://arxiv.org/abs/2206.11386

Bi-stochastic normalization of kernelized graph affinity matrix provides an
alternative normalization scheme for graph Laplacian methods in graph-based
data analysis and can be computed efficiently by Sinkhorn-Knopp (SK) iterations
in practice. This paper proves the convergence of the bi-stochastically
normalized graph Laplacian to manifold (weighted-)Laplacian with rates when $n$
data points are i.i.d. sampled from a general $d$-dimensional manifold embedded
in a possibly high-dimensional space. Under certain joint limit of $n \to
\infty$ and kernel bandwidth $\epsilon \to 0$, the …

arxiv bi convergence graph manifold math noise robustness