# Mind the Gap: A Study in Global Development through Persistent Homology

## TL;DR

This paper applies persistent homology, a topological data analysis technique, to study global development patterns using economic and health indicators, revealing hidden structures and relationships among countries.

## Contribution

It introduces a novel application of persistent homology to analyze global development data, uncovering multi-scale patterns and geographic cycles.

## Key findings

- Identification of localized development clusters
- Discovery of cycles related to geographic borders
- Revelation of hidden similarities among countries

## Abstract

The Gapminder project set out to use statistics to dispel simplistic notions about global development. In the same spirit, we use persistent homology, a technique from computational algebraic topology, to explore the relationship between country development and geography. For each country, four indicators, gross domestic product per capita; average life expectancy; infant mortality; and gross national income per capita, were used to quantify the development. Two analyses were performed. The first considers clusters of the countries based on these indicators, and the second uncovers cycles in the data when combined with geographic border structure. Our analysis is a multi-scale approach that reveals similarities and connections among countries at a variety of levels. We discover localized development patterns that are invisible in standard statistical methods.