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 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 …

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 …

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 …

Computational topology has recently seen an important development toward data analysis,
giving birth to Topological Data Analysis. Persistent homology appears as a fundamental …

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 …

The Euler characteristic is an invariant of a topological space that in a precise sense
captures its canonical notion of size, akin to the cardinality of a set. The Euler characteristic …

Topological data analysis and its main method, persistent homology, provide a toolkit for
computing topological information of high-dimensional and noisy data sets. Kernels for one …

A recurring task in mathematics, statistics, and computer science is understanding the
connectivity information, or equivalently, the topological properties of a given object. For …

Persistent homology is a method for probing topological properties of point clouds and
functions. The method involves tracking the birth and death of topological features as one …