Title: An Analysis of the Convergence of Graph Laplacians
Author: Daniel Ting, Ling Huang, and Michael Jordan
Abstract: Existing approaches to analyzing the asymptotics of 
graph Laplacians typically 
assume a well-behaved kernel function with smoothness
assumptions. We remove the smoothness assumption
and generalize the analysis of graph
Laplacians to include previously unstudied graphs
including kNN graphs.

We also introduce a kernel-free framework to analyze 
graph constructions with shrinking neighborhoods in general
and apply it to analyze locally linear embedding (LLE).

We also describe how for a given limiting Laplacian operator
desirable properties such as
a convergent spectrum and sparseness
can be achieved choosing the appropriate graph construction.
Date: July 2010