arXiv Machine Learning
Finite Topological Space Filtrations: A Topological Framework for Data Analysis
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arXiv Machine Learning
Jul 7
Topological data analysis using persistent discrete homology
arXiv:2506. 15020v2 Announce Type: replace-cross Abstract: We propose persistent discrete homology as a tool for topological data analysis and discuss its advantages over the existing methods.
arXiv Machine Learning
Jul 22
Topology-Driven Clustering: Enhancing Performance with Betti Number Filtration
arXiv:2505. 04346v2 Announce Type: replace Abstract: Clustering aims at partitioning data points into groups of similar objects without knowing about the class labels.
arXiv Machine Learning
5d ago
A New Non-archimedean Metric on Persistent Homology
The article introduces a new non‑archimedean metric, the cophenetic metric, defined on persistent homology classes of all degrees. It demonstrates that zeroth persistent homology combined with this metric and various hierarchical clustering algorithms yields statistically verifiable, commensurate topological information on multiple datasets. The resulting clusters, evaluated by silhouette score and Rand index, perform well, and the metric enables visualization of inter‑relations among persistent homology classes across all degrees via rooted trees.
arXiv AI
Aug 3
Dimensionality reduction for homological stability and global structure preservation
arXiv:2503. 03156v4 Announce Type: replace-cross Abstract: We propose DiRe, a force-directed dimensionality reduction framework designed to preserve global structure and homological features while remaining practical on modern hardware.
arXiv Machine Learning
Jun 11
From Persistence to Survival: Hypothesis Testing, Effect Sizes and Vectorisation for Topological Features
arXiv:2606. 11911v1 Announce Type: cross Abstract: Persistence diagrams are common representations in topological data analysis, but they do not naturally live in a vector space, and the statistical tools developed for comparing them have largely evolved separately from those used for downstream prediction.
arXiv AI
Jun 9
Topological Neural Operators
arXiv:2606. 09806v1 Announce Type: cross Abstract: We introduce Topological Neural Operators (TNOs), a principled framework for operator learning on cell complexes that lifts neural operators (NOs) from functions on points and/or edges to topological domains.