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 …

Comments• page viii, bottom of page: the following names should be added to the
acknowledgements:-Peter Landweber had an invaluable contribution to these notes. First …

Geometric and topological inference deals with the retrieval of information about a geometric
object using only a finite set of possibly noisy sample points. It has connections to manifold …

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 study the properties of the homology of different geometric filtered
complexes (such as Vietoris–Rips, Čech and witness complexes) built on top of totally …

Through the use of examples, we explain one way in which applied topology has evolved
since the birth of persistent homology in the early 2000s. The first applications of topology to …

Topological persistence has proven to be a key concept for the study of real-valued
functions defined over topological spaces. Its validity relies on the fundamental property that …

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 …

We introduce a family of signatures for finite metric spaces, possibly endowed with real
valued functions, based on the persistence diagrams of suitable filtrations built on top of …

Data often comes in the form of a point cloud sampled from an unknown compact subset of
Euclidean space. The general goal of geometric inference is then to recover geometric and …