ARTICLE
ABSTRACT
In the context of taxonomy methods in recent years, a lot of attention is paid to the stability of these methods, i.e. the answer to the question to what extent the structure discovered by a given method is actually present in the data? Many different ways of measuring stability have been proposed in the literature, which are mainly relating to the stability of the final grouping result. Lord et al. (2017) instead proposed a measure of stability for each observation from the data set and the measure of stability for individual groups. In their article, they suggest that an individual measure of stability may indicate noisy observation whereas the stability measure relating to particular groups may indicate clusters of noise which should be removed from the dataset. The aim of the paper is to apply the proposed individual measure of stability and a measure of stability for individual groups to answer the question to what extent Poland is matched the EU in terms of the level of sustainable development.
KEYWORDS
clustering, taxonomy, cluster stability, sustainable development
JEL
C38
REFERENCES
Ben-Hur A., Guyon I., (2003), Detecting Stable Clusters Using Principal Component Analysis, Methods in Molecular Biology, 224, 59–182.
Borys T., (red.), (2005), Wskaźniki zrównoważonego rozwoju, Wydawnictwo Ekonomia i Środowisko, Warszawa-Białystok, 41–43.
Borys T., (2014), Wybrane problemy metodologii pomiaru nowego paradygmatu rozwoju – polskie doświadczenia, Optimum. Studia Ekonomiczne, 3 (69), 3–21.
Brock G., Pihur V., Datta S., Datta, S., (2008), clValid: An R Package for Cluster Validation, Journal of Statistical Software, (25) 4.
Fang Y., Wang J., (2012), Selection of the Number of Clusters via the Bootstrap Method, Computational Statistics and Data Analysis, 56, 468–477.
Gajos E., (2017), Implementation of Selected Sustainable Development Objectives in European Union Countries, Zeszyty Naukowe Szkoły Głównej Gospodarstwa Wiejskiego w Warszawie. Problemy Rolnictwa Światowego, 17 (4), 68–77.
Górka K., (2007), Wdrażanie koncepcji rozwoju zrównoważonego i trwałego, Ekonomia i Środowisko, 2 (32), 8–20.
Hennig C., (2007), Cluster-wise Assessment of Cluster Stability, Computational Statistics and Data Analysis, 52, 258–271.
Katoła A., (2013), Poziom zrównoważonego rozwoju w Polsce i innych krajach Unii Europejskiej, Zeszyty Naukowe Uniwersytetu Szczecińskiego. Finanse, Rynki Finansowe, Ubezpieczenia, (57), 249–262.
Lord E., Willems M., Lapointe F. J., Makarenkov V., (2017), Using the Stability of Objects to Determine the Number of Clusters in Datasets, Information Sciences, 393, 29–46.
Lorek E., (2011), Ekonomia zrównoważonego rozwoju w badaniach polskich i niemieckich, w: Kos B., (red.), Transformacja gospodarki – poziom krajowy i międzynarodowy, Studia Ekonomiczne, Zeszyty Naukowe Uniwersytetu Ekonomicznego w Katowicach, 90, 103–112.
Shamir O., Tishby N., (2008), Cluster Stability for Finite Samples, Advances in Neural Information Processing Systems, 20, 1297–1304.
Suzuki R., Shimodaira H., (2006), Pvclust: An R Package for Assessing the Uncertainty in Hierarchical Clustering, Bioinformatics, 22 (12), 1540–2.
Teneta-Skwiercz D., (2018), Wskaźniki pomiaru zrównoważonego rozwoju – Polska na tle krajów Unii Europejskiej, Prace Naukowe Uniwersytetu Ekonomicznego we Wrocławiu, 516, 121–132.
Volkovich Z., Barzily Z., Toledano-Kitai D., Avros R., (2010), The Hotteling’s Metric as a Cluster Stability Measure, Computer Modelling and New Technologies, 14 (4), 65–72.
