## 4 Experimentation, Performance Evaluation, and Discussion
### Metrics for Performance Evaluation
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**High-Dimensional Datasets**} & \multicolumn{2}{c}{**HFA-K-Means**} & \multicolumn{2}{c}{**ISOSK-Means**} & \multicolumn{2}{c}{**PSODE**} & \multicolumn{2}{c}{**FADE**} & \multicolumn{2}{c}{**IWODE**} \\ \cline{2-10}  & **Mean** & **Std. Dev** & **Mean** & **Std. Dev** & **Mean** & **Std. Dev** & **Mean** & **Std. Dev** & **Mean** & **Std. Dev** \\ \hline A1 & **0.2942** & 0.0304 & 0.5911 & 0.0003 & 0.5949 & 0.0086 & 0.6171 & 0.0347 & 0.6525 & 0.0621 \\ A2 & **0.3155** & 0.0746 & 0.6781 & 0.0002 & 0.6912 & 0.0161 & 0.6976 & 0.0215 & 0.7296 & 0.0391 \\ A3 & 0.7915 & 0.0007 & 0.7945 & 0.0011 & 0.7106 & 0.0176 & **0.7085** & 0.0332 & 0.7527 & 0.0319 \\ Birch1 & 0.8001 & 0.0053 & 0.8030 & 0.0006 & 0.7256 & 0.0276 & **0.7232** & 0.0257 & 0.7692 & 0.0279 \\ Birch2 & **0.1904** & 0.0174 & 0.5071 & 0.0001 & 0.5070 & 0.0002 & 0.5155 & 0.0235 & 0.5176 & 0.0084 \\ Birch3 & **0.6577** & 0.0647 & 0.7168 & 0.0004 & 0.7074 & 0.0151 & 0.7012 & 0.0191 & 0.7570 & 0.0247 \\ Bridge & **0.3489** & 0.0132 & 0.6464 & 0.0009 & 0.7141 & 0.1007 & 0.6405 & 0.0709 & 1.1397 & 0.0666 \\ D31 & **0.6923** & 0.0658 & 0.8125 & 0.0070 & 0.8021 & 0.0407 & 0.7788 & 0.0376 & 0.7972 & 0.0514 \\ Dim002 & 0.7309 & 0.0000 & 0.6384 & 0.0222 & 0.5975 & 0.0445 & **0.6280** & 0.0607 & 0.6705 & 0.0432 \\ Dim1024 & **1.0698** & 0.1783 & 1.1332 & 0.3795 & 1.7644 & 0.0112 & 1.4759 & 0.1200 & 1.9654 & 0.0261 \\ Housec5 & **0.3255** & 0.0572 & 0.5377 & 0.0123 & 2.2408 & 4.0861 & 0.5467 & 0.0287 & 0.6865 & 0.0229 \\ Housec8 & **0.4164** & 0.0460 & 0.4919 & 0.5305 & 0.5022 & 0.0315 & 0.4707 & 0.0383 & 0.6344 & 0.0408 \\ Letter & **0.7921** & 0.0231 & 0.9683 & 1.0545 & 0.9121 & 0.0628 & 0.8665 & 0.0663 & 1.2057 & 0.0571 \\ Finland & **0.3061** & 0.0910 & 0.4427 & 0.0011 & 0.4465 & 0.0060 & 0.4686 & 0.0547 & 0.4864 & 0.0371 \\ S1 & 0.7714 & 0.0215 & 0.7770 & 0.0009 & **0.6739** & 0.0351 & 0.6756 & 0.0207 & 0.7501 & 0.0280 \\ S2 & 0.7332 & 0.1215 & 0.7412 & 0.0008 & **0.6844** & 0.0280 & 0.6939 & 0.0345 & 0.7556 & 0.0190 \\ S3 & **0.5073** & 0.0641 & 0.7126 & 0.0005 & 0.7106 & 0.0199 & 0.7072 & 0.0181 & 0.7559 & 0.0317 \\ S4 & 0.7645 & 0.0198 & 0.7723 & 0.0009 & **0.7299** & 0.0162 & 0.7356 & 0.0226 & 0.7896 & 0.0303 \\ T4.8k & **0.0218** & 0.0020 & 0.0227 & 0.0000 & 0.0227 & 0.0000 & 0.0423 & 0.0882 & 0.0928 & 0.0515 \\ Yeast & **0.5205** & 0.0570 & 0.7489 & 0.0682 & 0.7193 & 0.0677 & 0.6375 & 0.1344 & 0.5949 & 0.1144 \\ Average & **0.5526** & 0.0474 & 0.6768 & 0.1041 & 0.7729 & 0.2318 & 0.6665 & 0.0480 & 0.7752 & 0.0407 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of HFA-K-means with ISOS-K-means, PSODE, FADE, and IWODE on 20 high-dimensional datasets. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**High-Dimensional Datasets**} & \multicolumn{2}{c}{**HFA-K-Means**} & \multicolumn{2}{c}{**FAPSO**} & \multicolumn{2}{c}{**FADE**} & \multicolumn{2}{c}{**FATLBO**} \\ \cline{2-5}  & **Mean Value** & **Mean Value** & **Mean Value** & **Mean Value** \\ \hline Birch1 & 0.8001 & **0.6572** & 0.7232 & 0.6952 \\ Birch2 & **0.1904** & 0.5040 & 0.5155 & 0.5163 \\ Birch3 & **0.6577** & 0.6812 & 0.7012 & 0.7596 \\ Bridge & **0.3489** & 0.5901 & 0.6405 & 0.6108 \\ Housec5 & **0.3255** & 0.4187 & 2.2408 & 0.4158 \\ Housec8 & **0.4164** & 0.4245 & 0.5022 & 0.4559 \\ Letter & 0.7921 & **0.7146** & 0.9121 & 0.7775 \\ Average & 0.5046 & 0.5700 & 0.8908 & 0.6044 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison of HFA-K-means with FA-based hybrid algorithms: FAPSO, FADE, and FATLBO on seven high-dimensional datasets.