Comparação de métodos de agrupamentos hierárquicos aglomerativos em indicadores de sustentabilidade em municípios do estado do Pará

Abstract

This study aimed to compare the performance of hierarchical agglomerative clustering methods using a data set composed of several sustainability indicators referring to the municipalities of the state of Pará. As well as determining the number of initial groups to be formed by applying of validity indexes. For the selection of indicators, a check-list of national, regional and local scientific studies addressing the theme of sustainability was carried out. Subsequently, the indicators were standardized due to the units and scales of different measures, not interfering in the result and having similar weights in the calculation of the coefficient of similarity. The measure of dissimilarity used was the Euclidean distance, and to determine the hierarchical grouping method was used the agglomerative coefficient (AC). Validation indexes were used to establish the initial grouping number. The agglomerative method with the best performance regarding the (AL) was Ward with 0.94, indicating a better strength and quality among the agglomerative techniques. The Davies Bouldin (DB), Dunn (D) and Silhouette (SIL) validation indexes indicated that the ideal amount of initial clusters to be formed is 2, however the PBM index found that the ideal formation is with 4 groups. Regarding the municipalities with greater homogeneity, it was found that in the composition with 2 groups, the most similar observations were m105 (Salinópolis) and m109 (Santa Izabel do Pará), followed by the observations m102 (Rio Maria) and m144 (Xinguara), all inserted in group 1.

Sustainability assessment in cities in the eastern amazon

“…Still according to Figure 3, the results showed that Ward's structure was the one that presented the best performance and quality among the agglomerative methods in the dimensions because it presented values closer to 1, this fact was more evident in the general dimension that showed 80% more efficient than the others, and the simple method, which obtained the lowest value, is not indicated, as it has low efficiency, this is due to the fact that this method evaluates the smallest dissimilarity between the objects studied. The CA obtained in this research (0.99) was higher than the study by Crispim et al (2020), in which he obtained CA = 0.94 and equal to that obtained by Roth et al (2016), with CA = 0.99. Thus, the results indicate that this technique is the most appropriate to be used in the database related to sustainability indicators for the municipalities.…”

“…The need for normalization in the grouping method is related to the different scales and measures of the indicators, directly influencing the final result. Crispim et al (2020) addressed in their study that the measurement units after standardization have similar weights. Thus, the Range method was chosen for the normalization of the indicators, making the indicator vary between 0 and 1 (Equation ): where, Y is the value obtained through the range method; X is the value of the observed variable; min is the minimum of the observed variable; amp is the total amplitude of the observed variable.…”

“…It was decided to use the agglomerative hierarchical method to determine the number of groups, since it allows the formation of a tree diagram, in which similar observations are based on the indicators presented in the study (Crispim et al, 2020). According to Santos and Sousa (2018), the hierarchical method gathers data into groups, repeating this process at different levels, which will later form the dendrogram, also called a tree diagram.…”

“…The need for normalization in the grouping method is related to the different scales and measures of the indicators, directly influencing the final result. Crispim et al (2020) addressed in their study that the measurement units after standardization have similar weights. Thus, the Range method was chosen for the normalization of the indicators, making the indicator vary between 0 and 1 (Equation 1):…”

“…This theme needs an effective analysis through measurement methods that allow reaching a result closer to reality, however, there are many difficulties in finding adequate methodologies, since they must be distinct and subjective, and consider the social, economic, environmental and basic sanitation without any interference (Crispim et al, 2020; Rohan et al, 2018).…”