We study distributions of persistent homology barcodes associated to taking subsamples of
a fixed size from metric measure spaces. We show that such distributions provide robust …

We study distributions of persistent homology barcodes associated to taking subsamples of
a fixed size from metric measure spaces. We show that such distributions provide robust …

We show that an embedding in Euclidean space based on tropical geometry generates
stable sufficient statistics for barcodes. In topological data analysis, barcodes are multiscale …

Persistent homology allows us to create topological summaries of complex data. In order to
analyse these statistically, we need to choose a topological summary and a relevant metric …

A classical question about a metric space is whether Borel measures on the space are
determined by their values on balls. We show that for any given measure this property is …

We study the persistent homology of both functional data on compact topological spaces
and structural data presented as compact metric measure spaces. One of our goals is to …

We address the problem of estimating topological features from data in high dimensional
Euclidean spaces under the manifold assumption. Our approach is based on the …

Assume that a finite set of points is randomly sampled from a subspace of a metric space.
Recent advances in computational topology have provided several approaches to …

Topological data analysis (TDA) is a relatively new area of research related to importing
classical ideas from topology into the realm of data analysis. Under the umbrella term TDA …

Let P be a distribution with support S. The salient features of S can be quantified with
persistent homology, which summarizes topological features of the sublevel sets of the …