K-Means Clustering to Classify Indonesian Provinces Based on School Participation and Socio-Economic Indicators

Education serves as a fundamental pillar in national development, as it not only enhances individual capacities but also improves overall social welfare. Despite this crucial role, Indonesia continues to face disparities in both access to and quality of education among its regions, as can be seen from variations in school participation indicators and socio-economic backgrounds. To analyze these differences, this study applied the K-Means Clustering method to categorize provinces in Indonesia using six variables: School Participation Rate, Net Enrollment Rate, Gross Enrollment Rate, Poverty Rate, High School Ratio, and Teacher Ratio. To identify the most suitable number of clusters, three validation indices were utilized, namely Dunn Index, C-Index, and Davies-Bouldin Index, with cluster counts tested from three to six. The results indicated that the best clustering solution was five clusters, as reflected in the highest Dunn Index (0.1569), lowest C-Index (0.0321), and lowest Davies-Bouldin Index (0.5062). The robustness of this clustering was further supported by the ratio between within-cluster and between-cluster standard deviation (S(w)/S(b) = 0.33). Each cluster revealed unique characteristics of education and socio-economic conditions, where Cluster 4 displayed the most favorable outcomes with high participation and low poverty levels, whereas Cluster 5 highlighted the weakest performance across all observed indicators.