## 3 Results
### Cluster Methods Help Identifying the Multitarget Candidates  
All sets of the docking result were used to sequentially perform the cluster analysis using the 'factoextra' package in RStudio. First, the docked scores of all compounds were normalized to equal the weight of all groups. To define the optimal number of clusters (\(k\)), we used the average silhouette width and the most frequent indices as the parameters. The average silhouette method is used for evaluating the quality of clustering by computing the average observations (n) for different values of \(k\). Generally, the optimal number of clusters is the one that maximizes the average silhouette width over a range of possible values of clusters. Our results showed that two clusters maximize the average silhouette coefficients, with three clusters coming in as the second optimal number of clusters (Figure 4a). This study was in agreement with the result of the frequency among indices (Figure 4b). The bar plot indicated that the most frequent optimal number of clusters for all indices is two. No difference was observed in the result of both validation methods. We reasoned that the optimal number of clusters was defined into two clusters that possessed 82 and 26 in Cluster 1 (blue) and 2 (yellow), respectively. Further, the clustering data were visualized in the dimension plot (Figure 4c). A clustering data set performed the principal component analysis (PCA) to demonstrate the dominant features of this model and were plotted; the data points followed the first two principal components. These two PCs explain 98.5% of the point variability, which obtained the high variations of data. In addition, the hierarchical clustering algorithm was also used to confirm the accuracy of our clustering result. A hierarchical dendrogram helps in illustrating the clustering data, for which it was suggested that our data could be defined into two clusters (Figure 4d). Interestingly, the compounds with high binding affinities toward three receptors were placed in Cluster 2. Thus, we selected Cluster 2 for further analysis. Subsequently, all the observations in Cluster 2 were subjected to the subcluster analysis using the hierarchical k-means algorithm. This method uses a combination of the hierarchical and k-means algorithm to determine the cluster groups. The optimal numbers of clusters were defined as previously described. In the subclustering analysis, the proposed number of clusters was 3, according to the majority rules of all indices calculated from the nbclust package in R (Figure 5a). Afterward, the silhouette method was used to evaluate the quality of the clustering result (Figure 5b). This method calculates the distance between the clusters, called the silhouette width (Si). In general, a high value of Si suggests the well-clustered observation, whereas the negative value of the observation indicates that the observation may be placed in the wrong cluster. Then, the cluster groups of the observations were identified (Figure 5c). Figure 4: Clustering analysis of docking results. The numbers of clusters are identified using (**a**) average silhouette width and (**b**) frequency among all indices. The clustering shows two groups, indicating Cluster 1 (blue) and Cluster 2 (yellow). The groups of clusters are visualized in the (**c**) cluster plot generated by the K-means clustering method, and (**d**) a dendrogram generated by the hierarchical clustering method. Further, we performed a clustering heatmap plot. This method provides data visualization by color coding and correlation by using a dendrogram from the clustering method. The data from the subcluster analysis were prepared for a distance matrix prior to clustering into several groups using a hierarchical method. The subcluster data were clustered hierarchically by binding scores and by targets with color coding of dark green indicating high binding affinity and dark brown indicating low binding affinity (Figure 5d). It can be noted from the subcluster results that several compounds tended to cluster together.