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Documents authored by Bubenik, Peter

Artifact
Software
DOI: 10.4230/artifacts.26095
hubwag/Mixup-SoCG26

Authors: Hubert Wagner, Nickolas Arustamyan, Matthew Wheeler, and Peter Bubenik

Abstract
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Hubert Wagner, Nickolas Arustamyan, Matthew Wheeler, Peter Bubenik. hubwag/Mixup-SoCG26 (Software). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@misc{dagstuhl-artifact-26095,
   title = {{hubwag/Mixup-SoCG26}}, 
   author = {Wagner, Hubert and Arustamyan, Nickolas and Wheeler, Matthew and Bubenik, Peter},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:9b75232380440dc7556b698dd1b7d07882a61fac}{\texttt{swh:1:dir:9b75232380440dc7556b698dd1b7d07882a61fac}} (visited on 2026-05-27)},
   url = {https://github.com/hubwag/Mixup-SoCG26},
   doi = {10.4230/artifacts.26095},
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.94
Mixup Barcodes: Quantifying Geometric-Topological Interactions Between Point Clouds

Authors: Hubert Wagner, Nickolas Arustamyan, Matthew Wheeler, and Peter Bubenik

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
We propose a novel geometric-topological descriptor called a mixup barcode. Intuitively, it characterizes the shape of a point cloud as well as its spatial relationship with another point cloud embedded in the same ambient space. More technically, it enriches a standard persistence barcode with information on the image persistent homology. In three dimensions it captures natural spatial relationships like overlap and surrounding; in higher dimensions more intricate spatial relationships are captured. We provide a theoretical setup and a simple algorithm for mixup barcodes. As a proof of concept, we explore data arising in a geometric-topological problem from machine learning. Specifically, we take first steps towards verifying a hypothesis stating that geometric-topological relationships within intermediate point cloud representations in an artificial neural network can hinder its training. More broadly, our experiments suggest that mixup barcodes are useful for characterizing spatial relationships and spatial interactions (i.e. the evolution of spatial relationships) that are hard to directly visualize or capture using standard methods.
Cite as

Hubert Wagner, Nickolas Arustamyan, Matthew Wheeler, and Peter Bubenik. Mixup Barcodes: Quantifying Geometric-Topological Interactions Between Point Clouds. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 94:1-94:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{wagner_et_al:LIPIcs.SoCG.2026.94,
  author =	{Wagner, Hubert and Arustamyan, Nickolas and Wheeler, Matthew and Bubenik, Peter},
  title =	{{Mixup Barcodes: Quantifying Geometric-Topological Interactions Between Point Clouds}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{94:1--94:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.94},
  URN =		{urn:nbn:de:0030-drops-259009},
  doi =		{10.4230/LIPIcs.SoCG.2026.94},
  annote =	{Keywords: mixup barcode, persistent homology, persistence barcode, persistence diagram, image persistent homology, image persistence, deep learning, multilayer perceptron, topology of neural network embeddings, disentanglement}
}
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