Partitioning a Probability Distribution from a Sample using Laplacians

In this talk we will consider finding approximate isoperimetric partitions of a probability distributions given a sample from the distributions.  We first consider the case where we are explicitly given the distribution and discuss numerical methods to obtain Cheeger like cuts by reducing the problem to eigenvectors of a graph Laplacian.  Second, we look at known  unbiased estimators for estimating the PDF from a sample.  We will show how the second nearest neighbor estimators can be combine with mesh generation methods to construct a graph Laplacian from a sample.  Finally we will show some experimental results on partitioning flow cytometry data related to HIV.