99 citations · 157 across the 39 of their papers we have counts for
5 papers · 1 filter
Topological Community Detection: A Sheaf-Theoretic Approach
Arne Wolf, Anthea Monod
We propose a model for network community detection using topological data analysis, a branch of modern data science that leverages theory from algebraic topology to statistical ana…
Generalized Morse Theory of Distance Functions to Surfaces for Persistent Homology
Anna Song, Ka Man Yim, Anthea Monod
This paper brings together three distinct theories with the goal of quantifying shape textures with complex morphologies. Distance fields are central objects in shape representatio…
Stability for Inference with Persistent Homology Rank Functions
Qiquan Wang, Inés García-Redondo, Pierre Faugère +2
Persistent homology barcodes and diagrams are a cornerstone of topological data analysis that capture the "shape" of a wide range of complex data structures, such as point clouds,…
Probability Metrics for Tropical Spaces of Different Dimensions
Roan Talbut, Daniele Tramontano, Yueqi Cao +2
The problem of comparing probability distributions is at the heart of many tasks in statistics and machine learning. Established comparison methods treat the standard setting that…
Wavelet-Based Density Estimation for Persistent Homology
Konstantin Häberle, Barbara Bravi, Anthea Monod
Persistent homology is a central methodology in topological data analysis that has been successfully implemented in many fields and is becoming increasingly popular and relevant. T…