Persistent Homology (PH) is computationally expensive and cannot be
directly applied on more than a few thousand data points. This project
aims to develop mechanisms to allow the computation of PH on large,
high-dimensional data sets. The proposed method will significantly
reduce the run-time and memory requirements for the computation of PH
without significantly compromising accuracy of the results.

This project explores techniques to map a large point cloud P to
another point cloud P' with fewer total points such that the topology
space characterized by P and P' is nearly equivalent. The mapping from P
to P' will potentially hide some of the smaller topological features
during the PH computation on P'. Restoration of accurate PH results is
achieved by (i) upscaling data for the identified large topological
features, and (b) partition the data to run concurrent PH computations
that locate the smaller topological features.