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math.AT2025
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…
stat.ML2025
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…
math.AT2025
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…