Clustering Regency in Kalimantan Island Based on People's Welfare Indicators Using Ward's Algorithm with Principal Component Analysis Optimization

Abstract

Cluster analysis is used to group objects based on similar characteristics, so that objects in one cluster are more homogeneous than objects in other clusters. One method that is widely used in hierarchical clustering is Ward's algorithm. This method works by minimizing the sum of squared distances between objects in one cluster (within-cluster variance) to produce optimal clustering. However, one important assumption in using this method is that there is no high correlation between variables, or in other words, the data must be free from multicollinearity. Multicollinearity can cause distortion in distance calculation, resulting in less accurate clustering results. To overcome this problem, a Principal Component Analysis (PCA) approach is used to reduce the dimension and eliminate the correlation between variables by forming several mutually independent principal components. This research aims to cluster 56 districts/cities in Kalimantan Island based on 19 indicators of people's welfare in 2023, using Ward's algorithm optimized through PCA. Validation of clustering results is done using the Silhouette Coefficient value to assess the quality of clustering. This research method is a combination of Principal Component Analysis (PCA) and hierarchical clustering using Ward’s algorithm. PCA was applied to reduce 19 welfare-related indicators into four principal components that retained most of the essential information in the dataset. The clustering process based on these components resulted in two optimal clusters, as determined by a Silhouette Coefficient value of 0.651, which indicates a moderately strong cluster structure. The results of this research are that the first cluster consists of 47 districts/cities characterized by relatively low welfare levels, while the second cluster comprises 9 districts/cities with comparatively higher welfare conditions. These findings imply the existence of considerable disparities in welfare among regions on Kalimantan Island. The results can be used as a reference for policymakers in formulating more targeted and equitable development strategies