Multivariate Analysis of Regional Economic Resilience Capacity Using PCA, Gaussian Mixture Model, and Random Forest - Dian Septiana; Fanny Ramadhani; Sisti Nadia Amalia; Fahmi Ashari S. Sihaloho (Journal of Mathematics, Computations and Statistics, 2026)
Economic resilience capacity has become an important issue in regional development because socio-economic disparities influence the ability of regions to adapt to structural pressures and external disturbances. However, measuring regional resilience capacity remains challenging due to the multidimensional and interrelated nature of socio-economic indicators. This study analyses regional economic resilience capacity in North Sumatra using an integrated multivariate statistical and machine learning framework combining Principal Component Analysis (PCA), Gaussian Mixture Model (GMM), and Random Forest. PCA was employed to construct a composite Economic Resilience Capacity Index (ERCI) from socio-economic indicators, while GMM clustering was applied to identify regional typologies within the reduced dimensional space. The initial clustering estimation identified North Nias as an extreme singleton cluster, indicating the presence of an outlier observation. After excluding the outlier, the final GMM model selected a four-cluster spherical covariance structure based on the Bayesian Information Criterion (BIC). A comparison with K-means clustering produced different optimal grouping structures, indicating sensitivity to clustering assumptions and the complexity of regional socio-economic patterns. The first two principal components explained approximately 72% of the total variance, indicating adequate representation of the dominant socio-economic structure. The geographical distribution of clusters reveals substantial regional heterogeneity, where regions in the Nias area are concentrated within the low resilience capacity cluster, while urban and economically integrated regions form distinct growth-oriented clusters. Random Forest analysis indicates that unemployment and poverty related indicators are the most influential variables in distinguishing regional resilience typologies. Furthermore, the comparison between ERCI and GMM results shows that regions with relatively similar index values may still belong to different clusters, indicating that regional resilience patterns do not necessarily follow a single linear socio-economic structure. These findings suggest that regional economic resilience capacity in North Sumatra is shaped by multidimensional structural disparities rather than by a single composite index alone.