## 4 Performance Evaluation of Improved SOSK-Means
### Experiment 3  
In Experiment 3, the performance of the ISOSK-means algorithm on 23 real life datasets were evaluated. The computational results from the experiment under the DB validity index are shown in Table 8, showing the minimum, the maximum, the average, and the standard deviation scores for the ISOSK-means algorithm. The results were compared with other existing hybrid algorithms from the literature [61] for the same problem, as presented in Table 9. The ISOSK-means recorded a better mean value for the 23 real-life datasets than the other hybrid metaheuristic algorithms. This indicated that the improved hybrid algorithm performed better, on average, in solving the automatic clustering problem, compared with \begin{table}
\begin{tabular}{l l l l l l} \hline \hline  & \multicolumn{4}{c}{**ISOSK-Means (DB Index)**} \\
**Datasets** & **Min** & **Max** & **Mean** & **Std Dev** \\ \hline  
verage** & 0.7186 & 1.0350 & 0.8477 & 0.1452 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Computational results of ISOSK-means on 18 synthetic datasets. \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline  & \multicolumn{2}{c}{**ISOSK-Means**} & \multicolumn{2}{c}{**PSODE**} & \multicolumn{2}{c}{**FADE**} & \multicolumn{2}{c}{**IWODE**} \\  & **Mean** & **Std Dev** & **Mean** & **Std Dev** & **Mean** & **Std Dev** \\ \hline  
verage** & **0.8477** & 0.1452 & 0.9414 & 0.0565 & 0.8855 & 0.0593 & 1.1190 & 0.0354 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Performance comparison of ISOSK-means with other hybrid metaheuristic algorithms from literature on 18 synthetic datasets. the competing hybrid metaheuristic algorithms. However, it is worth noting that FADE had the best clustering result in nine of the datasets. Nevertheless, the ISOSK-means recorded the least standard deviation in 18 datasets, with the least mean standard deviation score in all, showing that it produced more compact clusters than the competing hybrid metaheuristic algorithms. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline  & \multicolumn{4}{c}{**ISOSK-Means (DB Index)**} \\
**Datasets** & **Min** & **Max** & **Mean** & **Std Dev** \\ \hline
**Aggregation** & 0.7229 & 0.7297 & 0.7262 & 0.0014 \\
**Breast** & 0.8121 & 0.8121 & 0.8121 & 0.0000 \\
**Bridge** & 0.6455 & 0.6474 & 0.6464 & 0.0009 \\
**Compound** & 0.4947 & 0.5033 & 0.4985 & 0.0021 \\
**D31** & 0.8016 & 0.8263 & 0.8125 & 0.0070 \\
**Flame** & 0.7748 & 0.7770 & 0.7760 & 0.0006 \\
**Glass** & 0.3612 & 0.7821 & 0.6547 & 0.1727 \\
**Housec5** & 0.5158 & 0.5650 & 0.5377 & 0.0123 \\
**Housec8** & 0.4919 & 0.5305 & 0.5158 & 0.0107 \\
**His** & 0.5913 & 0.6475 & 0.6165 & 0.0132 \\
**Jain** & 0.6495 & 0.6522 & 0.6507 & 0.0008 \\
**Leaves** & 0.7207 & 0.9591 & 0.7618 & 0.0745 \\
**Letter** & 0.9683 & 1.0545 & 1.0242 & 0.0188 \\
**Josensuu** & 0.5011 & 0.5147 & 0.5073 & 0.0038 \\
**Finland** & 0.4409 & 0.4453 & 0.4427 & 0.0011 \\
**Path-based** & 0.6533 & 0.6718 & 0.6669 & 0.0050 \\
**R15** & 0.7106 & 0.7771 & 0.7400 & 0.0171 \\
**Spiral** & 0.7320 & 0.7458 & 0.7386 & 0.0033 \\
**T4.sk** & 0.0227 & 0.0227 & 0.0227 & 0.0000 \\
**Thyroid** & 0.5692 & 0.6439 & 0.6039 & 0.0182 \\
**Wolbc** & 0.0508 & 0.0508 & 0.0508 & 0.0000 \\
**Wine** & 0.9414 & 1.0437 & 1.0053 & 0.0228 \\
**Veast** & 0.7084 & 0.8976 & 0.7489 & 0.0682 \\
**Average** & 0.6035 & 0.6652 & 0.6331 & 0.0198 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Computational results of ISOSK-means on 23 real-life datasets.