32 citations · 69 across the 25 of their papers we have counts for
5 papers · 1 filter
Proceedings of TDA: Applications of Topological Data Analysis to Data Science, Artificial Intelligence, and Machine Learning Workshop at SDM 2022
R. W. R. Darling, John A. Emanuello, Emilie Purvine +1
Topological Data Analysis (TDA) is a rigorous framework that borrows techniques from geometric and algebraic topology, category theory, and combinatorics in order to study the "sha…
Local Versus Global Distances for Zigzag Persistence Modules
Ellen Gasparovic, Maria Gommel, Emilie Purvine +4
This short note establishes explicit and broadly applicable relationships between persistence-based distances computed locally and globally. In particular, we show that the bottlen…
The Relationship Between the Intrinsic Cech and Persistence Distortion Distances for Metric Graphs
Ellen Gasparovic, Maria Gommel, Emilie Purvine +4
Metric graphs are meaningful objects for modeling complex structures that arise in many real-world applications, such as road networks, river systems, earthquake faults, blood vess…
Local homology of abstract simplicial complexes
Michael Robinson, Chris Capraro, Cliff Joslyn +4
This survey describes some useful properties of the local homology of abstract simplicial complexes. Although the existing literature on local homology is somewhat dispersed, it is…
A Complete Characterization of the 1-Dimensional Intrinsic Cech Persistence Diagrams for Metric Graphs
Ellen Gasparovic, Maria Gommel, Emilie Purvine +4
Metric graphs are special types of metric spaces used to model and represent simple, ubiquitous, geometric relations in data such as biological networks, social networks, and road…