A Class of Topological Pseudodistances for Fast Comparison of Persistence Diagrams

arXiv:2402.14489v1 Announce Type: cross
Abstract: Persistence diagrams (PD)s play a central role in topological data analysis, and are used in an ever increasing variety of applications. The comparison of PD data requires computing comparison metrics among large sets of PDs, with metrics which are accurate, theoretically sound, and fast to compute. Especially for denser multi-dimensional PDs, such comparison metrics are lacking. While on the one hand, Wasserstein-type distances have high accuracy and theoretical guarantees, they incur high computational cost. On …

abstract analysis applications arxiv class comparison computing cs.cg cs.cv cs.lg data data analysis diagrams math.at metrics persistence role sound type