A survey of topological machine learning methods
The last decade saw an enormous boost in the field of computational topology: methods and
concepts from algebraic and differential topology, formerly confined to the realm of pure …
concepts from algebraic and differential topology, formerly confined to the realm of pure …
Scalar field comparison with topological descriptors: Properties and applications for scientific visualization
In topological data analysis and visualization, topological descriptors such as persistence
diagrams, merge trees, contour trees, Reeb graphs, and Morse–Smale complexes play an …
diagrams, merge trees, contour trees, Reeb graphs, and Morse–Smale complexes play an …
Curvature filtrations for graph generative model evaluation
J Southern, J Wayland… - Advances in Neural …, 2023 - proceedings.neurips.cc
Graph generative model evaluation necessitates understanding differences between graphs
on the distributional level. This entails being able to harness salient attributes of graphs in …
on the distributional level. This entails being able to harness salient attributes of graphs in …
Persistence curves: A canonical framework for summarizing persistence diagrams
YM Chung, A Lawson - Advances in Computational Mathematics, 2022 - Springer
Persistence diagrams are one of the main tools in the field of Topological Data Analysis
(TDA). They contain fruitful information about the shape of data. The use of machine learning …
(TDA). They contain fruitful information about the shape of data. The use of machine learning …
On the stability of persistent entropy and new summary functions for topological data analysis
Persistent homology and persistent entropy have recently become useful tools for patter
recognition. In this paper, we find requirements under which persistent entropy is stable to …
recognition. In this paper, we find requirements under which persistent entropy is stable to …
Progressive wasserstein barycenters of persistence diagrams
This paper presents an efficient algorithm for the progressive approximation of Wasserstein
barycenters of persistence diagrams, with applications to the visual analysis of ensemble …
barycenters of persistence diagrams, with applications to the visual analysis of ensemble …
Cell cycle controls long-range calcium signaling in the regenerating epidermis
Skin homeostasis is maintained by stem cells, which must communicate to balance their
regenerative behaviors. Yet, how adult stem cells signal across regenerative tissue remains …
regenerative behaviors. Yet, how adult stem cells signal across regenerative tissue remains …
Filtration curves for graph representation
L O'Bray, B Rieck, K Borgwardt - Proceedings of the 27th ACM SIGKDD …, 2021 - dl.acm.org
The two predominant approaches to graph comparison in recent years are based on (i)
enumerating matching subgraphs or (ii) comparing neighborhoods of nodes. In this work, we …
enumerating matching subgraphs or (ii) comparing neighborhoods of nodes. In this work, we …
On the expressivity of persistent homology in graph learning
R Ballester, B Rieck - arXiv preprint arXiv:2302.09826, 2023 - arxiv.org
Persistent homology, a technique from computational topology, has recently shown strong
empirical performance in the context of graph classification. Being able to capture long …
empirical performance in the context of graph classification. Being able to capture long …
On the expressivity of persistent homology in graph learning
R Ballester, B Rieck - The Third Learning on Graphs Conference, 2024 - openreview.net
Persistent homology, a technique from computational topology, has recently shown strong
empirical performance in the context of graph classification. Being able to capture long …
empirical performance in the context of graph classification. Being able to capture long …