Triangulation Approach Using K-Means, Hierarchical Clustering, and DBSCAN for Beef Production Analysis

Abstract

This study implements a methodological triangulation approach for clustering highly skewed data using three algorithms with different paradigms: K-Means (partitional-based), Agglomerative Hierarchical Clustering with Ward Linkage (hierarchical-based), and DBSCAN (density-based). Applied to beef production data from 38 Indonesian provinces in 2024, the dataset exhibited extreme characteristics with a coefficient of variation of 171.89%, skewness of 2.87, and a maximum-minimum ratio of 664:1. Data were standardised using Z-score transformation to address scale differences. Evaluation using the Silhouette Score for K-Means and Hierarchical Clustering, alongside qualitative outlier detection with DBSCAN, revealed high consistency across all algorithms in identifying k=2 as the optimal structure, with a Silhouette Score of 0.9155. K-Means and Hierarchical Clustering produced identical groupings, separating three observations (7.89%) from 35 observations (92.11%), while DBSCAN confirmed this by explicitly labelling the three provinces as outliers. Robustness analysis via bootstrap resampling (100 iterations) demonstrated clustering stability with membership consistency of 99.7-100% and standard deviation of 0.0089. Sensitivity analysis validated the stability of outlier detection across the epsilon range 0.5-0.55. This research demonstrates that algorithmic triangulation provides robust cross-validation for data with extreme outliers, yielding consistent and stable clustering structures across sampling variation and parameter changes.