Comparison of Average Linkage and K-Means Methods in Clustering Indonesia’s Provinces Based on Welfare Indicators

Abstract

This study compares two clustering methods, i.e. average linkage and K-means, in grouping Indonesia’s provinces based on welfare indicators in education, health, and income. Data from Statistics Indonesia (BPS) covering Indonesia’s 34 provinces are used. Welfare variables exercised in this study are population, rate of population with government-assisted health covers, morbidity rate, human development index, expense rate per capita, and rate of the population aged 15 or over who graduated from junior high school (completed Year 9). Results show that the average linkage method generates three clusters; the first cluster of which consists of 32 provinces, while the second and third clusters each consist of only one province. On the other hand, the K-means method is set to generate equally three clusters. Unlike the first method, K-means’s first cluster, in this case, consists of 14 provinces, while its second and thirds clusters consist of 13 and 7 provinces, respectively. Performances of both methods are measured using the variance ratio. The average linkage and k-means cluster methods yield variance ratios of 0.08275 and 0.28881, respectively. Based on these criteria, the average linkage method is shown to exercise a better performance due to its smaller variance ratio.