An Analysis of the Convergence of Graph Laplacians

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.

• Type: Conference
• Year: 2010
• Where: ICML
• Authors: Daniel Ting, Ling Huang, Michael I. Jordan
• Keywords: Graph Construction, Graph Laplacians, ICML 2010, Machine Learning, Smoothness Assumption