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.
By Chris Kapulkin, Nathan Kershaw
arXiv:2512.23348v3 Announce Type: replace-cross
Abstract: We introduce a data-analysis framework based on filtrations of finite topological spaces. Starting from a finite metric data set, we construc...
By Sel\c{c}uk Kayacan
arXiv:2505. 04346v2 Announce Type: replace Abstract: Clustering aims at partitioning data points into groups of similar objects without knowing about the class labels.
By Arghya Pratihar, Kushal Bose, Swagatam Das
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.
By \.Ismail G\"uzel, Atabey Kaygun
arXiv:2507. 07156v2 Announce Type: replace-cross Abstract: Supervised machine learning pipelines trained on features derived from persistent homology have been experimentally observed to ignore much of the information contained in a persistence diagram.
By Nicole Abreu, Parker B. Edwards, Francis Motta
arXiv:2609.37177v1 Announce Type: cross
Abstract: Persistent homology (PH) is a frequently used tool for extracting and preserving topological information from image data, particularly in image segme...
By Alexander H. Berger, Marco Fontana, Daniel Rueckert, Johannes C. Paetzold, Laurin Lux, Ulrich Bauer