# Two Medoid-Based Algorithms for Clustering Sets
## 5 Clustering Results
\begin{table}
\begin{tabular}{l l l l l} \hline
**Dataset** & **SDM** & **ARI** & **CI** & **SI** & **Iterations** \\ \hline data\_1200\_100\_16\_5\_1 & 1513 & 0.99 & 0 & 0.71 & 2 \\ \hline data\_1200\_200\_4\_5\_1 & 7986 & 1.0 & 0 & 0.89 & 2 \\ \hline data\_1200\_200\_8\_5\_1 & 4827 & 0.99 & 0 & 0.79 & 1 \\ \hline data\_1200\_200\_16\_0\_1 & 1419 & 1.0 & 0 & 0.83 & 2 \\ \hline data\_1200\_200\_16\_5\_1 & 3126 & 0.99 & 0 & 0.68 & 1 \\ \hline data\_1200\_200\_16\_5\_2 & 3320 & 0.99 & 0 & 0.69 & 6 \\ \hline data\_1200\_200\_16\_5\_3 & 343a solution with minimal \(SDM\), highest \(ARI\), and \(CI=0\). This is due to the combination of design factors of the datasets, i.e., the number of clusters and the overlapping degree. By increasing the number of runs to \(10^{4}\), both the datasets were correctly handled by K-medoids with uniform random seeding, with a resultant solution for \(data\_1200\_200\_16\_40\_1\) which has minimal \(SDM\) = 3460, \(ARI\) = 0.99, \(CI\) = 0, and \(SI\) = 0.58, and an average \(ARI\) = 0.45, average \(CI\) = 3.85, and \(Success\)\(Rate\) = \(8\times 10^{-4}\). For the dataset \(data\_1200\_400\_16\_5\_1\), the emerged best solution has minimal \(SDM\) = 1824, \(ARI\) = 1.0, \(CI\) = 0, \(SI\) = 0.59, and average \(ARI\) = 0.53, average \(CI\) = 7.34, and \(Success\)\(Rate\) = \(7\times 10^{-4}\). The benefits of careful seeding are confirmed by all the results shown in Table 5.  
The results in Tables 6 and 7 are the average of 10 repetitions of the parallel random swap (\(PRS\)) algorithm. As one can see, the collected data agree with the results achieved by repeated K-medoids under the same seeding method. \(PRS\), though, was able to solve the clustering problem (\(CI=0\)) even under the uniform random initialization of medoids. In addition, using G-K-means++ significantly reduces the number of iterations the clustering solution requires to stabilize. Separate experiments were executed by using the modified Otsuka-Ochiai cosine distance. Except for the exact \(SDM\) values, which clearly depend on the specific distance measure adopted, the \(bARI\), \(bCI\), and \(bSI\) results are identical to the case the modified Jaccard distance was adopted, especially when the G-K-means++ seeding is used. Therefore, such results are not reported for brevity. For comparison purposes with the results documented in [8] and achieved by using K-sets and K-swaps, Table 8 collects the achieved clustering results when the number of clusters \(K\) varies from 4 to 32; Table 9 shows the results when the resolution \(L\) varies from 100 to 800; Table 10 reports the emerged data when the overlapping level \(o\) of clusters varies from 0% to 40%; and finally, Table 11 illustrates the results when the type of clusters \(t\) is varied from 1 to 5. The table results were confirmed by K-medoids and parallel random swap (\(PRS\)) under G-K-means++ seeding (GKM++). Since in [8] the \(CI\) and \(SI\) indexes were not reported, the table results show only the best-achieved \(ARI\) and the average \(ARI\) calculated along the values in a table row. In light of the data shown in Tables 8-11, the algorithms proposed in this paper for clustering sets are capable of generating solutions with the same accuracy as the approach described in [8], and in some cases can deliver better performance.