Comparison of agglomerative hierarchical clustering (AHC) algorithm and k-means algorithm in poverty data clustering in north sumatra

North Sumatra had the 17th lowest rate of poverty in 2023 out of 34 provinces, with 1,239.71 thousand people, or 8.15 percent, living there. Although there has been a decline in the poverty rate in 2023 compared to previous years, there are still many districts and cities in North Sumatra with significant rates of poverty; thus, this cannot be disregarded. The government must act to address this by providing the community with various forms of aid and increasing the number of job openings. To overcome this, one must first identify the cities or districts with the lowest to highest rates of poverty. This can be avoided with data mining, namely by applying the clustering technique. The Agglomerative Hierarchical Clustering (AHC) algorithm and the K-Means algorithm were the clustering techniques employed in this investigation. The Davies Bouldin Index (DBI) will then be used to validate the clustering results in order to ascertain which technique yields the best cluster. Three clusters were created using the AHC method: cluster 1 had 31 districts/cities, cluster 2 had one district/city, and cluster 3 had one district/city. Using the k-means approach, three clusters were identified: cluster 1, which included 22 districts/cities, had the lowest poverty rate; cluster 2, which included 10 districts/cities, had a moderate poverty rate; and cluster 3, which included 1 district/city, had the highest poverty rate. It was discovered through clustering validation that the k means method with a DBI value of 0.45 was the most effective approach for this investigation.