Data analysis using discrete cubical homology
This work provides a novel mathematical framework for data analysis, potentially benefiting researchers in fields like meteorology and finance by offering an alternative to existing methods.
The authors introduced persistence discrete homology as a new tool for data analysis, specifically designed to analyze filtrations of graphs, and applied it to high-dimensional data using pairwise correlations, with examples in weather and financial data compared to standard methods.
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.