Clustering of Central Java Districts Based on Educational Indicators: A Comparison of K-Means and Hierarchical Methods - Muhammad Syafiq; Nabila Fida Millati; Muh Akbar Idris; Anwar Fitrianto; Kevin Alifviansyah; Erfiani Erfiani (Jurusan Matematika FMIPA UNM, 2026)
This study aims to cluster districts and municipalities in Central Java based on educational indicators and to compare the clustering performance of K-Means and Hierarchical methods. The analysis uses secondary data from the Statistical Publication of Education in Central Java Province 2024, covering eight indicators related to educational facilities, participation, and attainment. The data were standardized, explored using descriptive statistics, and analyzed using K-Means and Hierarchical clustering methods. The evaluation results show that both methods produced broadly comparable clustering structures. However, Hierarchical Clustering demonstrated slightly stronger performance in terms of cluster separation and compactness, with a higher Silhouette Index (0,591) and Dunn Index (0,320) and a lower Davies–Bouldin Index (0,501) compared with K-Means (SI 0,584, Dunn 0,225, DBI 0,562). Meanwhile, K-Means produced a more balanced partition and a higher Calinski–Harabasz Index (48,63) than Hierarchical Clustering (44,30). The clustering results reveal a clear pattern of educational disparities across the region. A small group consisting of Sukoharjo Regency and the cities of Semarang, Surakarta, Salatiga, and Magelang forms a higher-performing cluster characterized by stronger educational indicators, while most rural districts belong to a lower-performing group. These findings indicate that educational disparities in Central Java remain spatially concentrated and highlight the need for targeted policies to strengthen educational investment and improve progression to higher levels of education in less developed districts.