ASAP-A sub-sampling approach for preserving topological structures modeled with geodesic topographic mapping

Topological data analysis tools enjoy increasing popularity in a wide range of applications, such as Computer graphics, Image analysis, Machine learning, and Astronomy for extracting information. However, due to computational complexity, processing large numbers of samples of higher dimensionality quickly becomes infeasible. This contribution is twofold: We present an efficient novel sub-sampling strategy inspired by Coulomb's law to decrease the number of data points in d-dimensional point clouds while preserving its homology. The method is not only capable of reducing the memory and computation time needed for the construction of different types of simplicial complexes but also preserves the size of the voids in d-dimensions, which is crucial e.g. for astronomical applications. Furthermore, we propose a technique to construct a probabilistic description of the border of significant cycles and cavities inside the point cloud. We demonstrate and empirically compare the strategy in several synthetic scenarios and an astronomical particle simulation of a dwarf galaxy for the detection of superbubbles (supernova signatures). (c) 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).

Automated summary

This article presents an efficient sub-sampling strategy for preserving homology in high-dimensional data. Additionally, a technique for probabilistic description of significant cycles and cavities in the data is proposed.