## 3 Proposed IBFO-KELM Model
\begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Step Size**} & \multicolumn{4}{c}{**IBFO-KELM**} \\ \cline{2-5}  & **ACC** & **MCC** & **Sensitivity** & **Specificity** \\ \hline
0.05 & 0.9213 (0.0389) & 0.8227 (0.0903) & 0.9679 (0.035) & 0.8286 (0.0768) \\
0.1 & 0.9402 (0.0362) & 0.8653 (0.0824) & 0.9713 (0.0282) & 0.8786 (0.0678) \\
0.15 & 0.9697 (0.0351) & 0.9243 (0.0907) & 0.9729 (0.0351) & 0.9600 (0.0843) \\
0.2 & 0.9476 (0.0512) & 0.8850 (0.1089) & 0.9679 (0.0544) & 0.9071 (0.0828) \\
0.25 & 0.9378 (0.0427) & 0.8614 (0.0965) & 0.9786 (0.0301) & 0.8571 (0.1117) \\
0.3 & 0.9211 (0.0377) & 0.8241 (0.0836) & 0.9675 (0.0365) & 0.8286 (0.1075) \\ \hline \end{tabular}
\end{table} 
Table 4: The classification results of IBPG-KELM (kernel extreme learning machine) with different chemotaxis step size. Figure 2: Convergence curves of the nine multidimensional benchmark functions for the four algorithms when dimension =2. and specificity of 80.50%. The GA-KELM yielded an ACC of 91.76%, 0.7775 MCC, sensitivity of 95.95%, and specificity of 80.00%. The Grid-KELM yielded the worst results with an ACC of 90.76%, 0.7592 MCC, sensitivity of 94.48%, and specificity of 79.00%. Figure 3 displays the surface of the training classification accuracies achieved by the KELM method for one fold via the grid search strategy, where the \(x\)-axis and \(y\)-axis are denoted by log2C and log2\(\gamma\), respectively. In addition, each mesh node in the plane (\(x,y\)) of the training accuracy represents a combination of the parameters, and the \(z\)-axis denotes the training accuracy value obtained with each combination of the parameters. In order to reveal subtle differences in the classification performance of the methods, the non-parametric statistical test [PERSON]'s rank-sum was used to check whether or not the improvement achieved by the IBPO-KELM was statistically significant. A \(p\)-value of less than 0.05 indicates statistical significance in the experiment. Table 6 shows that IBPO-KELM has significantly better results than the \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{4}{c}{**Metrics**} \\ \cline{2-5}  & **ACC** & **MCC** & **Sensitivity** & **Specificity** \\ \hline IBPO-KELM & 0.9697 \(\pm\) 0.0351 & 0.9243 \(\pm\) 0.0907 & 0.9729 \(\pm\) 0.0351 & 0.9600 \(\pm\) 0.0843 \\ BFO-KELM & 0.9329 \(\pm\) 0.0362 & 0.8280 \(\pm\) 0.0850 & 0.9586 \(\pm\) 0.0491 & 0.8550 \(\pm\) 0.1012 \\ PSO-KELM & 0.9282 \(\pm\) 0.0266 & 0.8056 \(\pm\) 0.0813 & 0.9657 \(\pm\) 0.0362 & 0.8050 \(\pm\) 0.1383 \\ GA-KELM & 0.9176 \(\pm\) 0.0662 & 0.7775 \(\pm\) 0.1879 & 0.9595 \(\pm\) 0.0349 & 0.8000 \(\pm\) 0.2494 \\ Grid-KELM & 0.9076 \(\pm\) 0.0679 & 0.7592 \(\pm\) 0.1637 & 0.9448 \(\pm\) 0.0724 & 0.7900 \(\pm\) 0.1647 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Classification performance obtained by the five methods in terms of ACC (classification accuracy), MCC (Matthew’s correlation coefficient), sensitivity, and specificity. Figure 3: Training accuracy surfaces of KELM and KELM with parameters obtained by the grid-search based KELM (Grid-KELM) for several folds. (**a**) Training accuracy surface of fold 2 for KELM; (**b**) Training accuracy surface of fold 4 for KELM; (**c**) Training accuracy surface of fold 6 for KELM; (**d**) Training accuracy surface of fold 8 for KELM. other four methods in terms of ACC and MCC. In Table 6, significant values that are greater than 0.05 are shown in bold. In order to describe the convergence of the proposed IBFO algorithm, we also recorded the trend that the accuracy (of the various KELM models based on swarm intelligence algorithms in the experiment) changed with population iteration. It is found from Figure 4 that the IBFO-KELM model can quickly converge to the best accuracy in the sixth iteration during the process of training, suggesting that the IBFO algorithm has a strong global search ability to avoid the algorithm being trapped prematurely in the local optimum.