hierarchical clustering

Thise study examines the tax capacity and tax effort of 149 countries, utilizing data envelopment analysis (DEA) combined with hierarchical clustering for differentiation.Tax capacity refers to the maximum potential tax revenue a country can achieve. While tax effort indicates the actual tax revenue collected relative to this potential. By categorizing countries into clusters, we uncover diverse levels of development and highlight strategies for improvement. Our methodology follows a four-step process involving correlation analysis, transformation of undesirable indicators, efficiency calculation, and rankings through the Anderson-Petersen method. Results reveal that economic indicators like GDP per capita influence tax capacities differently across nations. Some countries like Nepal and Mozambique outperform expectations in tax effort despite lower economic indicators, while others need significant policy reforms to optimize tax collection.

IntroductionNowadays, exploration of rare earth element (REE) resources is considered as one of the strategic priorities, which has a special position in the advanced and intelligent industries (Castor and Hedrick, 2006). Significant resources of REEs are found in a wide range of geological settings, including primary deposits associated with igneous and hydrothermal processes (e.g. carbonatite, (per) alkaline-igneous rocks, iron-oxide breccia complexes, scarns, fluorapatite veins and pegmatites), and secondary deposits concentrated by sedimentary processes and weathering (e.g. heavy-mineral sand deposits, fluviatile sandstones, unconformity-related uranium deposits, and lignites) (Jaireth et al., 2014). Recent studies on various parts of Iran led to the identification of promising potential of these elements, including Central Iran, alkaline rocks in the Eslami Peninsula, iron and apatite in the Hormuz Island, Kahnouj titanium deposit, granitoid bodies in Yazd, Azerbaijan, and Mashhad and associated dikes, and finally placers related to the Shemshak formation in Marvast, Kharanagh, and Ardekan indicate high concentration of REE in magmatogenic iron–apatite deposits in Central Iran and placers in Marvast area in Yazd (Ghorbani, 2013).
Materials and methodsIn the present study, the geochemical behavior of rare earth elements is modeled by using multivariate statistical methods in the eastern part of the Marvast placer. Marvast is located 185 km south of the city of Yazd in central Iran between Yazd and Mehriz. This area lies within the southeastern part of the Sanandaj-Sirjan Zone (Alipour-Asll et al., 2012). The samples of 53 wells were analyzed for Whole-rock trace-element concentrations (including REE) by inductively coupled plasma-mass spectrometry (ICP-MS) (GSI, 2004).
The clustering techniques such as multivariate statistical analysis technique can be employed to find appropriate groups in data sets. One of the main objectives of data clustering is to maximize both the similarity within each cluster and the difference between clusters, and finally find the structure in the data. Nowadays, cluster analysis is applied in many disciplines: biology, botany, medicine, psychology, geography, marketing, image processing, psychiatry, archaeology, etc. (Everitt et al., 2011). To execute a partitioning algorithm, the principal components analysis (PCA) algorithm is applied for feature selection, feature extraction and dimension reduction. Hierarchical clustering can be utilized to provide a nested sequence of partitions with bottom-up or top-down methods based on similarity. The single linkage and complete linkage are the most popular hierarchical algorithms (Jain et al., 1999; Ji et al., 2007).
Results and discussionThe REE chondrite-normalized pattern for the eastern area in the Marvast placer represents a high match to the standard pattern of monazite. This pattern shows the positive anomaly of Ce and the negative anomaly of Eu. To determine the distribution of REEs concentration, 2D interpolation maps were plotted in three groups of light, middle, and heavy REEs (LREE, MREE, and HREE), which were indicated in the geochemical anomaly at the south and south-west of the area. The relative ratios of (LREE/HREE) and (Ce/Eu) exposed the high proportion of LREEs to HREEs. In the next section, the hierarchical clustering algorithm was employed to partition the data in the feature and sample levels. The elements portioning demonstrated four separated groups, which can be related to atomic and chemical structures. The studied region was divided into four zones by the clustering approach. The fourth zone confine coincided with the REE anomaly area. Finally, PCA was applied as the multivariate statistical tool to this dataset. Hence three principal components modeled over 90% of the variance. For the first component, the distribution map of load factor has a good agreement with anomaly area.

Rock typing by different techniques is useful to interpret the zoning of reservoir. As the hydraulic flow unit has an effective connectionbetween the geological and petrophysical conditions, recognition of distribution quality of flow units in a reservoir can be useful for separation of reservoir into different units with different reservoir conditions. In this study, by using of flow zone indicator (FZI), six flow units has been determined based on the porosity and permeability data in both wells A and B of the Bangestan reservoir in the MansouriOil Field. The main statistical parameters of Porosity and permeability data for each of flow units (HFU) shows HFU3andHFU1 have the highest and HFU5 and HFU6 have the lowest reservoir quality in the oil field. In order to cluster validity, silhouette approach was used to hierarchical and K-means clustering methods and finally hierarchical clustering was selected as the best method and the porosity and permeability data for both wells were included in the six clusters (RT). Comparison between Hierarchical clustering method with the flow units and microfacies indicated acceptable results for both methods.

Hierarchical and K-mean clustering, according to their ability to meet the needs and problems of research in several scientific disciplines, are widely used among researchers. Extensive use of clustering in different contexts of health, engineering, social sciences and humanities, lead to growth of knowledge in these sciences. R, SAS and MATLAB software are the most widely used software in the analysis of clustering because of their ability in programming. However, each of this software has particular ability and limitations to clustering. So the familiarity of researcher with clustering method in each of this software allows them to use software which meets their needs for performing hierarchical clustering and K-means.