Gaussian Mixture Models for Human Development-Based Regional Clustering of East Java - Didik Bani Unggul; Muhammad Rusli Baharuddin; Miftah Fahira; Muhammad Zulfadhli (Sciencestatistics: Journal of Statistics, Probability, and Its Application, 2026)
Regional disparities in human development require an analytical approach that can identify latent patterns in development achievements. This study applies the Gaussian Mixture Model (GMM) to cluster regencies and cities in East Java based on the Human Development Index (HDI). GMM was chosen because it offers a probabilistic and distribution-based clustering framework, assigns regions using posterior membership probabilities, and provides interpretable parameters such as mixing proportions, component means, and variances. Univariate GMMs with two, three, and four components were fitted to HDI data from 38 regencies/cities in East Java at two time points, 2015 and 2025, which represent a ten-year interval. Model selection was conducted using internal cluster-validity measures, namely the Silhouette Coefficient and the Davies–Bouldin Index. The results show that the two-component GMM is selected as the best model for both years. The selected model produces the same membership structure in 2015 and 2025, forming a larger cluster of 31 regencies/cities with relatively lower and more variable HDI values and a smaller cluster of 7 regencies/cities with higher and more homogeneous HDI values. Over the ten-year interval, HDI increased in all regions, while the two-cluster structure remained evident. These findings can support regional development planning, policy evaluation, and the formulation of more targeted development strategies across regencies and cities.