## 4 Performance Evaluation of Improved SOSK-Means
### Experiment 1  
In the first set of experiments conducted, the improved SOSK-means was run on 12 datasets, initially used for the SOSK-means. These were Breast, Compound, Flame, Glass, Iris, Jain, Path-based, Spiral, Thyroid, Two moons, Wine, and Yeast datasets. The experimental results are summarized in Table 4, showing the values obtained by the ISOSK-means for each of the 12 datasets. The four decimal place values represented the minimum, the maximum, the mean value over 40 simulations and the standard deviations, which measured the range of values the algorithm converged. From the results obtained, the ISOSK-means returned the best mean values for four of the datasets (Compound, Jain, Thyroid, and two-moons) under the DB index, and eight of the datasets (Breast, Flame, Glass, Iris, Path-based, Spiral, Wine and Yeast) had the best mean values under the CS index. The average computational time for achieving convergence for each dataset by the improved algorithm is shown in Figure 3. Even though the CS index returned the best overall average results for the 12 datasets, this was at the expense of higher computational time. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**DB Index**} & \multicolumn{3}{c}{**CS Index**} \\
**Datasets** & **Min** & **Max** & **Mean** & **Std Dev** & **Min** & **Max** & **Mean** & **Std Dev** \\ \hline
**Breast** & 0.8121 & 0.8121 & 0.8121 & 0.0000 & 0.5996 & 0.7209 & **0.6639** & 0.0391 \\
**Compound** & 0.4947 & 0.5033 & **0.4985** & 0.0021 & 0.4995 & 0.5032 & 0.5031 & 0.0006 \\
**Flame** & 0.7748 & 0.7770 & 0.7760 & 0.0006 & 0.3846 & 0.3846 & **0.3846** & 0.0000 \\
**Glass** & 0.3612 & 0.7821 & 0.6547 & 0.1727 & 0.0608 & 0.0608 & **0.0608** & 0.0000 \\
**Iris** & 0.5913 & 0.6475 & 0.6165 & 0.0132 & 0.5311 & 0.5821 & **0.5510** & 0.0118 \\
**Jain** & 0.6495 & 0.6522 & **0.6507** & 0.0008 & 0.6546 & 0.6546 & 0.6546 & 0.0000 \\
**Path-based** & 0.6533 & 0.6718 & 0.6669 & 0.0050 & 0.5588 & 0.6494 & **0.6289** & 0.0299 \\
**Spiral** & 0.7320 & 0.7458 & 0.7386 & 0.0033 & 0.5861 & 0.6862 & **0.6618** & 0.0329 \\
**Thyroid** & 0.5692 & 0.6439 & **0.6039** & 0.0182 & 0.6409 & 0.6409 & 0.6409 & 0.0000 \\
**Two moons** & 0.6008 & 0.6033 & **0.6021** & 0.0006 & 0.7176 & 0.7482 & 0.7243 & 0.0113 \\
**Wine** & 0.9414 & 1.0437 & 1.0053 & 0.0228 & 0.6570 & 0.8625 & **0.7614** & 0.0571 \\
**Yeast** & 0.3560 & 0.9902 & 0.8019 & 0.1407 & 0.3897 & 0.5110 & **0.4777** & 0.0252 \\
**Average** & 0.6280 & 0.7394 & 0.7023 & 0.0317 & **0.5234** & 0.5837 & **0.5594** & 0.0173 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Computational results for improved SOSK-means on 12 real-life datasets. Figure 3: Computational time for the ISOSK-means. Table 5 summarizes the simulated results for each of the four competing algorithms for the automatic clustering of the 12 real-life datasets. The results present the mean and the standard deviation for each algorithm. The values were obtained for the two cluster validity indices, the DB index, and the CS index. As shown in Table 5, the ISOSK-means had the best mean score under the DB validity index in 11 of the 12 datasets, with a tie on the Breast dataset for three of the algorithms: ISOSK-means, SOSK-means and K-means. In the same vein, the ISOSK-means recorded the best mean scores under the CS validity index for the ISOSK-means in eight datasets with ties for two of the algorithms: SOSK-means and ISOSK-means, in four of the datasets (Flame, Glass, Jain, and Thyroid). The performance analysis of the four competing algorithms is shown in Figures 4 and 5 for each cluster validity index. These results indicated that the ISOSK-means algorithm performed better than the other three competing algorithms. The average execution times of the SOS, SOSK-means and ISOSK-means algorithms for 200 generations were presented separately for each validity index, as shown in Figures 6 and 7. As expected, being a non-hybrid algorithm, the SOS recorded the lowest computational time under the two validity indices.