We present an algorithm for the computation of Vietoris–Rips persistence barcodes and
describe its implementation in the software Ripser. The method relies on implicit …

The computation of Vietoris-Rips persistence barcodes is both execution-intensive and
memory-intensive. In this paper, we study the computational structure of Vietoris-Rips …

Persistent homology (PH) matrix reduction is an important tool for data analytics in many
application areas. Due to its highly irregular execution patterns in computation, it is …

We show that recent results on randomized dimension reduction schemes that exploit
structural properties of data can be applied in the context of persistent homology. In the spirit …

The boundary matrix serves as a crucial representation for computing the persistence
diagrams, which is a typical topological data analysis method, and its reduction is the most …

The twenty-first century is a data-driven era where human activities and behavior, physical
phenomena, scientific discoveries, technology advancements, and almost everything that …

Persistent Homology (PH) analysis is a powerful tool for understanding many relevant
topological features from a given dataset. PH allows finding clusters, noise, and relevant …

Topological data analysis (TDA) based on persistent homology (PH) has become
increasingly popular in automation technology. Recent advances in imaging and simulation …

Persistent homology, first developed at the beginning of the millennium, is a tool within the
field of topological data analysis. It is an extension of simplicial homology to filtrations of …

A common topological data analysis approach used in the experimental sciences involves
creating machine learning pipelines that incorporate discriminating topological features …