## 4 Experimentation, Performance Evaluation, and Discussion
### Metrics for Performance Evaluation
This is presented in Figure 3. The computation results of the HFA-K-means are compared with the classical FA and K-means algorithms. The summary of the results obtained by the proposed HFA-K-means compared with the classical FA and K-means algorithm for the problem at hand over 20 high-dimensional datasets is presented in Table 6.  
The performance of the HFA-K-means is also compared with results from the literature. The mean and standard deviation metrics from experiments in this study and that available in the literature are used for the comparisons. There are three categories of comparisons with results from the literature. The first category compares with classical metaheuristics algorithms GA, DE, PSO, and IWO. This is presented in Table 7. The second category compares HFA-K-means with other hybrid metaheuristics algorithms: ISOSK-means, PSODE, FADE, and IWODE, as shown in Table 8. A comparison with other FA-based hybrid metaheuristics are presented in Table 8. \begin{table}
\begin{tabular}{l l} \hline
**Metaheuristic-Based K-Means Hybrid Algorithm** & **Mean Rank** \\ \hline
**HFAK-means** & 2.48 \\
**HTLBOK-means** & 3.21 \\
**HDEK-means** & 3.36 \\
**HPSOK-means** & 3.67 \\
**HIWOK-means** & 4.90 \\
**HSOSK-means** & 5.62 \\
**HABCK-means** & 6.29 \\
**HGAK-means** & 6.48 \\ \hline \end{tabular}
\end{table} 
Table 4: Friedman mean rank for the eight metaheuristic-based K-mean hybrid algorithms. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**High-Dimensional Datasets**} & \multicolumn{4}{c}{**DB Index**} \\ \cline{2-5}  & **Best** & **Worst** & **Mean** & **Std. Dev** \\ \hline A1 & 0.2441 & 0.3503 & 0.2942 & 0.0304 \\ A2 & 0.2186 & 0.4406 & 0.3155 & 0.0746 \\ A3 & 0.7908 & 0.7922 & 0.7915 & 0.0007 \\ Birch1 & 0.7774 & 0.8018 & 0.8001 & 0.0053 \\ Birch2 & 0.1585 & 0.2154 & 0.1880 & 0.0198 \\ Birch3 & 0.6130 & 0.7160 & 0.6539 & 0.0421 \\ Bridge & 0.3289 & 0.3714 & 0.3489 & 0.0132 \\ D31 & 0.5773 & 0.7929 & 0.6923 & 0.0658 \\ Dim002 & 0.7309 & 0.7309 & 0.7309 & 0.0000 \\ Dim1024 & 0.3717 & 1.1511 & 1.0698 & 0.1783 \\ Housec5 & 0.2465 & 0.4808 & 0.3255 & 0.0572 \\ Housec8 & 0.3131 & 0.4720 & 0.4164 & 0.0460 \\ Letter & 0.7548 & 0.8157 & 0.7921 & 0.0231 \\ Finland & 0.2042 & 0.4789 & 0.3061 & 0.0910 \\ S1 & 0.6801 & 0.7767 & 0.7714 & 0.0215 \\ S2 & 0.5412 & 0.9898 & 0.7332 & 0.1215 \\ S3 & 0.3782 & 0.6038 & 0.5073 & 0.0641 \\ S4 & 0.6802 & 0.7690 & 0.7645 & 0.0198 \\ T4.8k & 0.0178 & 0.0227 & 0.0218 & 0.0020 \\ Yeast & 0.4379 & 0.5559 & 0.5205 & 0.0570 \\ Average & 0.4544 & 0.6164 & 0.5522 & 0.0464 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Computation result for Improved FA-K-means on twenty high-dimensional datasets. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**HFA-K-Means**} & \multicolumn{4}{c}{**FA**} & \multicolumn{4}{c}{**K-Means**} \\ \cline{2-13}
**High-Dimensional Datasets** & \multicolumn{1}{c}{**Best**} & **Worst** & **Mean** & \multicolumn{1}{c}{**Std. **} & \multicolumn{1}{c}{**Dev**} & **Best** & **Worst** & **Mean** & \multicolumn{1}{c}{**Std. **} & \multicolumn{1}{c}{**Dev**} & **Best** & **Worst** & **Mean** & \multicolumn{1}{c}{**Std. **} \\  & & & & & & & & & & Dev & & Dev \\ \hline A1 & 0.2441 & 0.3503 & **0.2942** & 0.0304 &  
In comparing the performance of the proposed HFA-K-means with other algorithms, the solution quality determined by the DBI, which was used as the clustering objective during the program execution, was used. The clustering solutions are recorded using four decimal place values, and optimal clustering solutions are marked in boldface to indicate which algorithm produced the optimal clustering solution for each dataset. For validating the significant difference between the clustering results produced by the separate algorithms statistically, the [PERSON] statistical test with the [PERSON] post hoc test was performed. The results of both tests are presented and recorded in Tables 10 and 11, respectively.