Interfaculty Institute of Mathematics and Statistics, Calisia University-Kalisz, 62-800 Kalisz, Poland.
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, 61-614 Poznań, Poland.
Int J Environ Res Public Health. 2020 Sep 25;17(19):7021. doi: 10.3390/ijerph17197021.
The aim of this study was to investigate if the macroregions of Poland are homogeneous in terms of the observed spatio-temporal data characterizing their sustainable development. So far, works related to the sustainable development of selected territorial units have been based on data relating to a specific year rather than many years. The solution to the problem of macroregion homogeneity goes through two stages. In step one, the original spatio-temporal data space (matrix space) was transformed into a kernel discriminant coordinates space. The obtained kernel discriminant coordinates function as synthetic measures of the level of sustainable development of Polish macroregions. These measures contain complete information on the values of 27 diagnostic features examined over 15 years. In the second step, cluster analysis was used in order to identify groups of homogeneous macroregions in the space of kernel discriminant coordinates. The agglomeration method and the Ward method were chosen as commonly used methods. By means of both methods, three super macroregions composed of homogeneous macroregions were identified. Within the kernel discriminant coordinates, the differentiating power of a selected set of 27 features characterizing the sustainable development of macroregions was also assessed. To this end, five different and most commonly used methods of discriminant analysis were used to test the correctness of the classification. Depending on the method, the classification errors amounted to zero or were close to zero, which proves a well-chosen set of diagnostic features. Although the data relate only to a specific country (Poland), the presented statistical methodology is universal and can be applied to any territorial unit and spatial-temporal dynamic data.
本研究旨在探讨波兰的大区在观察到的描述其可持续发展的时空数据方面是否具有同质性。到目前为止，与选定的地域单元的可持续发展相关的工作都是基于特定年份的数据，而不是多年的数据。解决大区同质性问题需要经过两个阶段。在第一阶段，将原始的时空数据空间（矩阵空间）转换为核判别坐标空间。得到的核判别坐标函数作为波兰大区可持续发展水平的综合测度。这些测度包含了 15 年来 27 个诊断特征值的完整信息。在第二阶段，使用聚类分析来识别核判别坐标空间中同质性大区的群组。选择了凝聚方法和 Ward 方法作为常用方法。通过这两种方法，识别出了三个由同质大区组成的超级大区。在核判别坐标中，还评估了用于描述大区可持续发展的一组 27 个特征的区分能力。为此，使用了五种不同的、最常用的判别分析方法来检验分类的正确性。根据方法的不同，分类错误为零或接近零，这证明了所选诊断特征的合理性。虽然数据仅涉及特定国家（波兰），但所提出的统计方法具有普遍性，可应用于任何地域单元和时空动态数据。
