Cubical Homology of Graphs for Data Analysis

Discrete cubical homology is a graph invariant that detects combinatorial higher-dimensional holes in a graph. I will introduce this invariant and report on joint work with Nathan Kershaw (arXiv:2410.09939) on efficiently computing cubical homology of graphs. Subsequently, I will discuss an ongoing project, also joint with Kershaw, applying these techniques to data analysis, in particular, the weather and stock market data.