Data analysis using discrete cubical homology

TL;DR

This paper introduces persistence discrete homology, a novel method for analyzing high-dimensional data through graph filtrations, demonstrating its effectiveness in weather and financial data analysis compared to standard techniques.

Contribution

The paper presents a new tool called persistence discrete homology for data analysis, specifically tailored for graph filtrations and high-dimensional data representation.

Findings

Effective analysis of weather data using the new method.

Successful application to financial data analysis.

Comparison shows advantages over standard methods.

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.