In topological data analysis (TDA), one often studies the shape of data by constructing a
filtered topological space, whose structure is then examined using persistent homology …

PERSISTENT HOMOLOGY: THEORY AND PRACTICE HERBERT EDELSBRUNNER IST
Austria, Am Campus 1, 3400 Klosterneuburg, Austria, Duke Unive Page 1 PERSISTENT …

The continued and dramatic rise in the size of data sets has meant that new methods are
required to model and analyze them. This timely account introduces topological data …

Persistence theory emerged in the early 2000s as a new theory in the area of applied and
computational topology. This book provides a broad and modern view of the subject …

Our intention, at the beginning, was to write a short paper resolving some technical issues in
the theory of topological persistence. Specifically, we wished to present a clean easy-to-use …

The Handbook of Linear Algebra provides comprehensive coverage of linear algebra
concepts, applications, and computational software packages in an easy-to-use handbook …

We present the main algorithmic and design choices that have been made to represent
complexes and compute persistent homology in the Gudhi library. The Gudhi library …

In this paper we discuss the adaptation of the methods of homology from algebraic topology
to the problem of pattern recognition in point cloud data sets. The method is referred to as …

We describe a new methodology for studying persistence of topological features across a
family of spaces or point-cloud data sets, called zigzag persistence. Building on classical …

In 2009, Chazal et al. introduced ϵ ϵ-interleavings of persistence modules. ϵ ϵ-
interleavings induce a pseudometric d_ I d I on (isomorphism classes of) persistence …