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 …

Topological data analysis (TDA) can broadly be described as a collection of data analysis
methods that find structure in data. These methods include clustering, manifold estimation …

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 …

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 …

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 …

Many applications in science and engineering require a digital model of a real physical
object. Advanced scanning technology has made it possible to scan such objects and …

One of the most elusive challenges within the area of topological data analysis is
understanding the distribution of persistence diagrams arising from data. Despite much effort …

Optimization is concerned with choosing several variables to optimize (maximize or
minimize) an objective function, usually subject to several constraints. In the last twenty-five …