ASAP - A Sub-sampling Approach for Preserving Topological Structures

Topological data analysis tools enjoy increasing popularity in a wide range of applications. However, due to computational complexity, processing large number of samples of higher dimensionality quickly becomes infeasible. We propose a 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. We demonstrate and compare the strategy in several synthetic scenarios and an astronomical particle simulation of a Jellyfish galaxy for the detection of superbubbles (supernova signatures).