Divorce Determinants Clustering in Indonesia Using K-Means and Agglomerative Hierarchical Methods (AHC) - Danang Hilal Kurniawan; Nurul Alfajar Gumel; David Boby C. Nainggolan; M. Syamsuddin Wisnubroto; Fajri Farid (Politeknik Negeri Batam, 2026)
This study evaluates the spatial typologies of marital dissolution across 34 Indonesian provinces through a dual algorithm computational framework. By applying a proportional ratio transformation, demographic bias generated by absolute population disparities is mathematically eliminated, enabling an objective spatial analysis of 13 specific divorce determinants. Agglomerative Hierarchical Clustering (AHC) and K-Means algorithms are integrated to assess structural validity. The optimal spatial partitioning is established at k=4, empirically supported by the inflection point on the Within Cluster Sum of Squares (WCSS) curve at 9.7238 and a stable Silhouette Score of 0.2417. Structural consistency between the hierarchical and partitional models is validated by an Adjusted Rand Index (ARI) of 0.7931. Statistical profiling based on centroid matrices stratifies the regions into four distinct typologies, Cluster 0 (Moderate Multi Factor) exhibiting moderately distributed determinants, Cluster 1 (High Risk Deviant Behavior) characterized by average centroid scores exceeding 0.70 for variables including drug abuse, gambling, and forced marriage, Cluster 2 (Economic Driven) demonstrating an absolute dominance in economic factors with a centroid score of 0.9152, and Cluster 3 (Conflict Pure) fundamentally driven by continuous disputes with a centroid score of 0.7787. These structural configurations mathematically verify that marital dissolution in Indonesia is geographically stratified by highly specific socioeconomic, behavioral, and relational variables.