非线性生活质量指数
Nonlinear Quality of Life Index
摘要：
我们提出了171个国家的非线性生活质量指数的分析细节。该指数基于四个指标：按购买力平价计算的人均国内生产总值、出生时预期寿命、婴儿死亡率和结核病发病率。我们分析的数据结构，以找到最佳的和独立的专家意见的方式来映射几个数字指标从多维空间到一维空间的生活质量。在4D空间中，我们发现了一条主曲线，它“穿过”数据集的中间，并将数据点投影在这条曲线上。沿着这条主曲线的顺序为我们提供了国家的排名。投影到主曲线上提供了对对象的无监督排序的经典问题的解决方案。它使我们能够找到独立于专家意见的方法，将多个数字指标从多维空间投影到指标值的一维空间。在某种意义上，这种投影是最优的，并且保留了尽可能多的信息。对于计算，我们使用ViDaExpert，这是一种用于多维矢量数据可视化和分析的工具（arXiv：1406.5550）。
英文摘要：
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).
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