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Open AccessArticle

Sustainable Development of Polish Macroregions—Study by Means of the Kernel Discriminant Coordinates Method

1
Interfaculty Institute of Mathematics and Statistics, Calisia University-Kalisz, 62-800 Kalisz, Poland
2
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, 61-614 Poznań, Poland
3
Faculty of Social Sciences, Calisia University-Kalisz, 62-800 Kalisz, Poland
4
Faculty of Economic, The Great Poland Socio-Economic University, 63-000 Środa Wlkp., Poland
*
Author to whom correspondence should be addressed.
Int. J. Environ. Res. Public Health 2020, 17(19), 7021; https://doi.org/10.3390/ijerph17197021
Received: 30 July 2020 / Revised: 17 September 2020 / Accepted: 18 September 2020 / Published: 25 September 2020
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. View Full-Text
Keywords: sustainable development; spatio-temporal data; NUTS-1; kernel discriminant coordinates method; super macroregions sustainable development; spatio-temporal data; NUTS-1; kernel discriminant coordinates method; super macroregions
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Krzyśko, M.; Wołyński, W.; Ratajczak, W.; Kierczyńska, A.; Wenerska, B. Sustainable Development of Polish Macroregions—Study by Means of the Kernel Discriminant Coordinates Method. Int. J. Environ. Res. Public Health 2020, 17, 7021.

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