With the recent explosion in the amount, the variety, and the dimensionality of available
data, identifying, extracting, and exploiting their underlying structure has become a problem …

We define a new topological summary for data that we call the persistence landscape. Since
this summary lies in a vector space, it is easy to combine with tools from statistics and …

A thoroughly revised and updated edition of this introduction to modern statistical methods
for shape analysis Shape analysis is an important tool in the many disciplines where objects …

Confidence sets for persistence diagrams Page 1 The Annals of Statistics 2014, Vol. 42, No.
6, 2301–2339 DOI: 10.1214/14-AOS1252 © Institute of Mathematical Statistics, 2014 …

Given a distribution ρ ρ on persistence diagrams and observations X_ 1, ..., X_ n ∼\limits^
iid ρ X 1,…, X n∼ iid ρ we introduce an algorithm in this paper that estimates a Fréchet …

This paper shows that the space of persistence diagrams has properties that allow for the
definition of probability measures which support expectations, variances, percentiles and …

We introduce a statistic, the persistent homology transform (PHT), to model surfaces in and
shapes in. This statistic is a collection of persistence diagrams—multiscale topological …

Persistent homology captures the evolution of topological features of a model as a
parameter changes. The most commonly used summary statistics of persistent homology are …

We study the expected topological properties of Čech and Vietoris–Rips complexes built on
random points in ℝ d. We find higher-dimensional analogues of known results for …

Persistence landscapes map persistence diagrams into a function space, which may often
be taken to be a Banach space or even a Hilbert space. In the latter case, it is a feature map …