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 …

In this article, we extend the notions of dominated vertex and strong collapse of a simplicial
complex as introduced by J. Barmak and E. Miniam. We say that a simplex (of any …

We introduce a fast and memory efficient approach to compute the persistent homology (PH)
of a sequence of simplicial complexes. The basic idea is to simplify the complexes of the …

It has been observed since a long time that data are often carrying interesting topological
and geometric structures. Characterizing such structures and providing efficient tools to infer …

This paper is a continuation of the research reported in [7] on the usage of strong collapses
to accelerate the computation of persistent homology (PH). We show that further decisive …

Topological Data Analysis (TDA) is an emergent field that aims to discover topological
information hidden in a dataset. TDA tools have been commonly used to create filters and …

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 …

Abstract Topological Data Analysis (TDA) characterizes data based on topological invariants
present in the data. In general, TDA treats the data as a discrete sampling of an underlying …

In this paper, we introduce a fast and memory efficient approach to compute the Persistent
Homology (PH) of a sequence of simplicial complexes. The basic idea is to simplify the …

Matrix reduction is the standard procedure for computing the persistent homology of a
filtered simplicial complex with m simplices. Its output is a particular decomposition of the …