7 papers
Persistent Homology for Labeled Datasets: Gromov-Hausdorff Stability and Generalized Landscapes
Yaoying Fu, Evgeniya Lagoda, Shiying Li +3
Techniques from metric geometry have become fundamental tools in modern mathematical data science, providing principled methods for comparing datasets modeled as finite metric spac…
Metrics for Parametric Families of Networks
Mario Gómez, Guanqun Ma, Tom Needham +1
We introduce a general framework for analyzing data modeled as parameterized families of networks. Building on a Gromov-Wasserstein variant of optimal transport, we define a family…
Conic Formulations of Transport Metrics for Unbalanced Measure Networks and Hypernetworks
Mary Chriselda Antony Oliver, Emmanuel Hartman, Tom Needham
The Gromov-Wasserstein (GW) variant of optimal transport, designed to compare probability densities defined over distinct metric spaces, has emerged as an important tool for the an…
Stability of Hypergraph Invariants and Transformations
Tom Needham, Ethan Semrad
Graphs are fundamental tools for modeling pairwise interactions in complex systems. However, many real-world systems involve multi-way interactions that cannot be fully captured by…
Geometry of the Space of Partitioned Networks: A Unified Theoretical and Computational Framework
Stephen Y Zhang, Fangfei Lan, Youjia Zhou +4
Interactions and relations between objects may be pairwise or higher-order in nature, and so network-valued data are ubiquitous in the real world. The "space of networks", however,…
Topological Optimal Transport for Geometric Cycle Matching
Stephen Y Zhang, Michael P H Stumpf, Tom Needham +1
Topological data analysis is a powerful tool for describing topological signatures in real world data. An important challenge in topological data analysis is matching significant t…
Interleaving Distances, Monoidal Actions and 2-Categories
Patrick K. McFaddin, Tom Needham
Interleaving distances are used widely in Topological Data Analysis (TDA) as a tool for comparing topological signatures of datasets. The theory of interleaving distances has been…