Topological methods such as persistent homology are powerful tools for data
analysis of high-dimensional data sets but these methods almost exclusively
rely on thresholding techniques. However, in noisy data sets thesholding does
not always allow for the recovery of topological information. We present a
computationally-efficient algorithm to allow for topological data analysis on
noisy high-dimensional point cloud data sets. In many cases, the algorithm
returns data that has so few outliers that there is no need to threshold the
data before performing topological analysis.