A Comparative Study of Clustering Algorithms for Indonesian Provincial Food Security

Food security disparities in Indonesia remain multidimensional and spatially uneven, requiring analytical approaches that can capture regional differences beyond single indicators. This study compares multiple clustering algorithms to classify 38 Indonesian provinces using twelve food security indicators representing food availability, affordability, utilization, and consumption outcomes. Provincial secondary data for 2024 were obtained from official sources, including Statistics Indonesia, the National Food Agency, and the Ministry of Health. The analysis began with data standardization and Principal Component Analysis, which retained three components explaining 74.65% of total variance. Ten clustering approaches were then evaluated, including K-Means, hierarchical linkage methods, Fuzzy C-Means, DBSCAN, HDBSCAN, Gaussian Mixture Model, and ensemble clustering. Each solution was assessed using internal validity indices, including Silhouette, Davies–Bouldin, and Dunn Index, as well as degeneracy checks, cluster membership consistency, bootstrap stability analysis based on ARI and NMI, robustness checks under alternative preprocessing and variable subsets, and substantive interpretability. Ward Linkage was selected as the final method because it produced a non-degenerate and interpretable three-cluster typology, supported by similar partitions from Complete Linkage and ensemble clustering. The two-province high-vulnerability cluster persisted under log-transformation of skewed indicators, removal of individual variables, and reduced component dimensionality. The final clusters reveal clear territorial disparities: a relatively food-secure cluster covering most western and central provinces, a moderately vulnerable eastern cluster, and a high-vulnerability cluster consisting of Papua Pegunungan and Papua Selatan. Poverty, electricity access, protein consumption, health service burden, stunting, and life expectancy were the strongest differentiating indicators. These findings demonstrate the value of combining internal validity and stability analysis to support robust provincial food security typologies and targeted regional policy interventions.