Data analysis using discrete cubical homology

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.

@article{kapulkin2025_2506.15020,
  title={ Data analysis using discrete cubical homology },
  author={ Chris Kapulkin and Nathan Kershaw },
  journal={arXiv preprint arXiv:2506.15020},
  year={ 2025 }
}