Nonlinear Quality of Life Index

TL;DR

This paper introduces a nonlinear, data-driven approach to ranking countries based on a multidimensional quality of life index using principal curves, providing an optimal and unbiased ranking method.

Contribution

It proposes a novel unsupervised ranking method using principal curves to map multiple indicators onto a single quality of life index, independent of expert opinion.

Findings

Identified a principal curve through the data that captures the structure of the indicators.

Projected countries onto this curve to derive a ranking that preserves maximum information.

Demonstrated the method's effectiveness using the ViDaExpert tool.

Abstract

We present details of the analysis of the nonlinear quality of life index for 171 countries. This index is based on four indicators: GDP per capita by Purchasing Power Parities, Life expectancy at birth, Infant mortality rate, and Tuberculosis incidence. We analyze the structure of the data in order to find the optimal and independent on expert's opinion way to map several numerical indicators from a multidimensional space onto the one-dimensional space of the quality of life. In the 4D space we found a principal curve that goes "through the middle" of the dataset and project the data points on this curve. The order along this principal curve gives us the ranking of countries. Projection onto the principal curve provides a solution to the classical problem of unsupervised ranking of objects. It allows us to find the independent on expert's opinion way to project several numerical indicators from a multidimensional space onto the one-dimensional space of the index values. This projection is, in some sense, optimal and preserves as much information as possible. For computation we used ViDaExpert, a tool for visualization and analysis of multidimensional vectorial data (arXiv:1406.5550).