The Application of Silhouette Coefficient, Elbow Method, and Gap Statistics for Determining the Optimal Clusters in Grouping Provinces in Indonesia Based on Happiness Index
Abstract
Currently, the assessment of regional development success is still limited to economic growth and poverty factors. However, evaluation based solely on economic factors is not accurate enough because high economic growth does not always guarantee the happiness of society and can even worsen social inequality. Therefore, one of the important priorities in development is to create economic growth that can improve the welfare of society equally, without creating gaps between social groups. The well-being and social progress in a region can be influenced by the happiness of its people. Happiness can be used as a measure to assess the welfare obtained by individuals. In this study, clustering of happiness index based on provinces in Indonesia was conducted using the K-Means algorithm in RStudio. Through the K-Means clustering analysis, the results of this study can be used as a reference by the government in formulating strategic plans or making improvements to increase the level of happiness and welfare of the Indonesian society. There are three methods to determine the optimal number of clusters: Silhouette method, Elbow method, and Gap Statistics. In the comparison of methods, it is observed that the optimal cluster formation occurs with 2 clusters, where the Elbow and Silhouette methods yield the best results. The data was processed using the K-Means method, resulting in 2 groups: 16 provinces with a high-level happiness group and 18 provinces with a low-level happiness group. From the evaluation using the Silhouette Index, a value of 0.4005945 was obtained at k=2, indicating that this cluster falls into the weak structure category.
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