42 citations · 110 across the 13 of their papers we have counts for
5 papers · 1 filter
Stratified Formal Deformations and Intersection Homology of Data Point Clouds
Markus Banagl, Tim Mäder, Filip Sadlo
Intersection homology is a topological invariant which detects finer information in a space than ordinary homology. Using ideas from classical simple homotopy theory, we construct…
Topological Machine Learning with Persistence Indicator Functions
Bastian Rieck, Filip Sadlo, Heike Leitte
Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distanc…
Hierarchies and Ranks for Persistence Pairs
Bastian Rieck, Filip Sadlo, Heike Leitte
We develop a novel hierarchy for zero-dimensional persistence pairs, i.e., connected components, which is capable of capturing more fine-grained spatial relations between persisten…
Persistence Concepts for 2D Skeleton Evolution Analysis
Bastian Rieck, Filip Sadlo, Heike Leitte
In this work, we present concepts for the analysis of the evolution of two-dimensional skeletons. By introducing novel persistence concepts, we are able to reduce typical temporal…
Persistent Intersection Homology for the Analysis of Discrete Data
Bastian Rieck, Markus Banagl, Filip Sadlo +1
Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample…