Data analysis using discrete cubical homology

Chris Kapulkin, Nathan Kershaw
6/17/2025
math.ATcs.LGmath.CO

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Abstract

We present a new tool for data analysis: persistence discrete homology, which is well-suited to analyze filtrations of graphs. In particular, we provide a novel way of representing high-dimensional data as a filtration of graphs using pairwise correlations. We discuss several applications of these tools, e.g., in weather and financial data, comparing them to the standard methods used in the respective fields.

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Cite this paper

@article{kapulkin2025data,
  title  = {Data analysis using discrete cubical homology},
  author = {Chris Kapulkin and Nathan Kershaw},
  year   = {2025},
  eprint = {2506.15020},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2506.15020v1}
}

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