An Analysis of the Convergence of Graph Laplacians

Description: 

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 limit operator, desirable properties such as a convergent spectrum and sparseness can be achieved by choosing the appropriate graph construction

Authors: 
Daniel Ting
Ling Huang
Michael Jordan
Publication Date: 
Tuesday, June 1, 2010
Publication Information: 
International Conference on Machine Learning (ICML), June 2010