Computational Experiments on Random Chromatic Persistent Homology

Sophie Rosenmeier, Ondřej Draganov, Morteza Saghafian, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner
Proceedings of the Geometry, Topology, and Machine Learning Workshop, PMLR 325:269-276, 2026.

Abstract

Chromatic alpha complexes serve as a generalization of alpha complexes for chromatic point sets and were developed beyond two colors by \citet{Cult25}. Instead of only one as in the case in standard persistent homology, six different persistence diagrams result from this construction. Here we present the findings of \citet{Rose25}, in which we study the expected number and total length of persistence pairs for each diagram, assuming uniformly distributed $2$-colored points in the unit square. Additionally, we highlight deeper connections to the research area of Euclidean minimum spanning trees.

Cite this Paper

BibTeX
@InProceedings{pmlr-v325-rosenmeier26a, title = {Computational Experiments on Random Chromatic Persistent Homology}, author = {Rosenmeier, Sophie and Draganov, Ond\v{r}ej and Saghafian, Morteza and Cultrera di Montesano, Sebastiano and Edelsbrunner, Herbert}, booktitle = {Proceedings of the Geometry, Topology, and Machine Learning Workshop}, pages = {269--276}, year = {2026}, editor = {Bleher, Michael and Jensen, Freya and Maier, Levin and Taha, Diaaeldin and Wienhard, Anna}, volume = {325}, series = {Proceedings of Machine Learning Research}, month = {10--14 Nov}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v325/main/assets/rosenmeier26a/rosenmeier26a.pdf}, url = {https://proceedings.mlr.press/v325/rosenmeier26a.html}, abstract = {Chromatic alpha complexes serve as a generalization of alpha complexes for chromatic point sets and were developed beyond two colors by \citet{Cult25}. Instead of only one as in the case in standard persistent homology, six different persistence diagrams result from this construction. Here we present the findings of \citet{Rose25}, in which we study the expected number and total length of persistence pairs for each diagram, assuming uniformly distributed $2$-colored points in the unit square. Additionally, we highlight deeper connections to the research area of Euclidean minimum spanning trees.} }
Endnote
%0 Conference Paper %T Computational Experiments on Random Chromatic Persistent Homology %A Sophie Rosenmeier %A Ondřej Draganov %A Morteza Saghafian %A Sebastiano Cultrera di Montesano %A Herbert Edelsbrunner %B Proceedings of the Geometry, Topology, and Machine Learning Workshop %C Proceedings of Machine Learning Research %D 2026 %E Michael Bleher %E Freya Jensen %E Levin Maier %E Diaaeldin Taha %E Anna Wienhard %F pmlr-v325-rosenmeier26a %I PMLR %P 269--276 %U https://proceedings.mlr.press/v325/rosenmeier26a.html %V 325 %X Chromatic alpha complexes serve as a generalization of alpha complexes for chromatic point sets and were developed beyond two colors by \citet{Cult25}. Instead of only one as in the case in standard persistent homology, six different persistence diagrams result from this construction. Here we present the findings of \citet{Rose25}, in which we study the expected number and total length of persistence pairs for each diagram, assuming uniformly distributed $2$-colored points in the unit square. Additionally, we highlight deeper connections to the research area of Euclidean minimum spanning trees.
APA
Rosenmeier, S., Draganov, O., Saghafian, M., Cultrera di Montesano, S. & Edelsbrunner, H.. (2026). Computational Experiments on Random Chromatic Persistent Homology. Proceedings of the Geometry, Topology, and Machine Learning Workshop, in Proceedings of Machine Learning Research 325:269-276 Available from https://proceedings.mlr.press/v325/rosenmeier26a.html.

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