HYDROGEOLOGICAL CLUSTER ANALYSIS WITH AVERAGE LINKAGE AND WARD METHOD IN THE SOUTHERN SLOPE OF MERAPI MOUNTAIN

Abstract

This study aims to see the cluster analysis process using the average linkage method and the Ward method, and comparing thus results in analysis to clustering several related variables deciding to use the data of depth and hydro chemical character of groundwater. Processing cluster analysis with the average linkage method is pairing objects that combine into one cluster. Then, calculating the two proximity of the object to another variable, the next merging occurs in the most similar clusters than other variables, forming the second cluster. The second combination is to calculate using the average linkage method formula, forming a new distance matrix. The cluster analysis steps with the Ward method starts by the close look at N clusters, which have one respondent for each cluster (all variables consider cluster). The first cluster is formed by selecting two of these N groups, which, when combined, have the smallest value of Error Sum of Squares (SSE). N-1 clusters then consider again to determine which of these two clusters can minimize heterogeneity. Thus, N clusters are systematically reduced by N-1, become N-2, and so on until they become one cluster. The results of clustering the two methods compared with the criteria for standard deviation within groups (S_W) and standard deviation between groups (S_B). The best method has a smaller S_W and S_B ratio. The results showed that the average linkage method and the Ward method have an S_B and S_W ratio value. This result shows that the average linkage method has better performance than the Ward method.