arXiv:1702.08593math.AT
Mind the Gap: A Study in Global Development through Persistent Homology
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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.
There are a number of approaches; since it's still relatively new, there's a lot of "playing around" with techniques. 1) The first idea is to just see which topological features persist as the filtration/threshold parameter varies. I personally find the barcode illustration…
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