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.
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Notes
- 1.
Free material from www.gapminder.org.
- 2.
Gross Domestic Product per capita by Purchasing Power Parities (in international dollars, fixed 2011 prices). The inflation and differences in the cost of living between countries has been taken into account [19].
- 3.
The average number of years a newborn child would live if current mortality patterns were to stay the same [20].
- 4.
The probability that a child born in a specific year will die before reaching the age of one, if subject to current age-specific mortality rates. Expressed as a rate per 1000 live births [10].
- 5.
Gross national income converted to international dollars using purchasing power parity rates [22].
- 6.
Most data comes from years 2015, 2016, with others as early as 2005. See Table 8 in Appendix 1.
- 7.
- 8.
The choice of six is to coincide with the six clusters in the Gapminder project, see Fig. 1.
- 9.
The clustering presented in Appendix 2 results in different clusters, which more closely align with this simplistic notion.
- 10.
The generating countries are not guaranteed to be minimal in a geometric sense; they can make up any loop through the connected component that contains the homology class. One can find the minimal loop by examining the weight of its internal edges.
- 11.
There is a slight deviation from monotonic decrease in life expectancy at Peru. These deviations are not uncommon, but do not detract from the maximal-minimal pattern we observe.
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Banman, A., Ziegelmeier, L. (2018). Mind the Gap: A Study in Global Development Through Persistent Homology. In: Chambers, E., Fasy, B., Ziegelmeier, L. (eds) Research in Computational Topology. Association for Women in Mathematics Series, vol 13. Springer, Cham. https://doi.org/10.1007/978-3-319-89593-2_8
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